The XXZ model

In this file we will give step by step instructions on how to analyze the spin 1/2 XXZ model. The necessary packages to follow this tutorial are:

using MPSKit, MPSKitModels, TensorKit, Plots

Failure

First we should define the hamiltonian we want to work with. Then we specify an initial guess, which we then further optimize. Working directly in the thermodynamic limit, this is achieved as follows:

H = heisenberg_XXX(; spin=1 // 2);

We then need an intial state, which we shall later optimize. In this example we work directly in the thermodynamic limit.

random_data = TensorMap(rand, ComplexF64, ℂ^20 * ℂ^2, ℂ^20);
state = InfiniteMPS([random_data]);

The groundstate can then be found by calling find_groundstate.

groundstate, cache, delta = find_groundstate(state, H, VUMPS());

[ Info: VUMPS init:	obj = +2.499971249561e-01	err = 4.8102e-03
[ Info: VUMPS   1:	obj = -1.047871149491e-01	err = 3.6332884520e-01	time = 0.08 sec
[ Info: VUMPS   2:	obj = -2.424105097429e-01	err = 3.6011566451e-01	time = 0.02 sec
┌ Warning: ignoring imaginary component 1.475763903743127e-6 from total weight 2.0662736930482595: operator might not be hermitian?
│   α = 0.8739699649778873 + 1.475763903743127e-6im
│   β₁ = 1.345735500203679
│   β₂ = 1.3017908581601034
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.1833380872891541e-6 from total weight 2.0507172924982444: operator might not be hermitian?
│   α = 0.7372884749735164 + 1.1833380872891541e-6im
│   β₁ = 1.3017908581601034
│   β₂ = 1.4025646794468833
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2416644342636007e-6 from total weight 2.031220380535854: operator might not be hermitian?
│   α = 0.7386571067649788 + 1.2416644342636007e-6im
│   β₁ = 1.4025646794468833
│   β₂ = 1.2700607201611787
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3004780743588323e-6 from total weight 1.9679978250135914: operator might not be hermitian?
│   α = 0.7393243960693548 + 1.3004780743588323e-6im
│   β₁ = 1.2700607201611787
│   β₂ = 1.3089540265940922
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6458907476889217e-6 from total weight 2.0349614523247865: operator might not be hermitian?
│   α = 0.7249377970347587 + 1.6458907476889217e-6im
│   β₁ = 1.3089540265940922
│   β₂ = 1.3791927563392283
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.368995952526035e-6 from total weight 2.054876147824496: operator might not be hermitian?
│   α = 0.7217714242687149 + 1.368995952526035e-6im
│   β₁ = 1.3791927563392283
│   β₂ = 1.3414131857361027
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2494864182130416e-6 from total weight 2.0096836188378915: operator might not be hermitian?
│   α = 0.807454611112027 + 1.2494864182130416e-6im
│   β₁ = 1.2894881464660273
│   β₂ = 1.313036792683791
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.1639985493788058e-6 from total weight 2.0933444093691493: operator might not be hermitian?
│   α = 0.8461206485955095 + 1.1639985493788058e-6im
│   β₁ = 1.313036792683791
│   β₂ = 1.3935942900696372
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.141568236568552e-6 from total weight 2.0729883136407588: operator might not be hermitian?
│   α = 0.5431648307956423 + 1.141568236568552e-6im
│   β₁ = 1.3935942900696372
│   β₂ = 1.435321382047205
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6521519737508483e-6 from total weight 2.060744558293663: operator might not be hermitian?
│   α = 0.5404024011086792 + 1.6521519737508483e-6im
│   β₁ = 1.435321382047205
│   β₂ = 1.376403251103502
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6923960462905674e-6 from total weight 1.9964796296703375: operator might not be hermitian?
│   α = 0.6219891554004395 + 1.6923960462905674e-6im
│   β₁ = 1.376403251103502
│   β₂ = 1.3055935403492547
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.5709160999938243e-6 from total weight 2.0472728905311404: operator might not be hermitian?
│   α = 0.8795272048710723 + 1.5709160999938243e-6im
│   β₁ = 1.3055935403492547
│   β₂ = 1.3088864318921027
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3793371174981167e-6 from total weight 2.008276861479189: operator might not be hermitian?
│   α = 0.7608179355505824 + 1.3793371174981167e-6im
│   β₁ = 1.3088864318921027
│   β₂ = 1.3195257972863235
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6662444934072845e-6 from total weight 1.9904775101744567: operator might not be hermitian?
│   α = 0.6960250799777928 + 1.6662444934072845e-6im
│   β₁ = 1.3195257972863235
│   β₂ = 1.3177258731789887
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.8182383051540407e-6 from total weight 1.9900059862237078: operator might not be hermitian?
│   α = 0.7703642977709004 + 1.8182383051540407e-6im
│   β₁ = 1.3177258731789887
│   β₂ = 1.2768168220529936
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3705999932014934e-6 from total weight 1.9641339239991362: operator might not be hermitian?
│   α = 0.6373205365232443 + 1.3705999932014934e-6im
│   β₁ = 1.2768168220529936
│   β₂ = 1.3495863840638673
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2716514099669375e-6 from total weight 2.021948581163632: operator might not be hermitian?
│   α = 0.6621740011024483 + 1.2716514099669375e-6im
│   β₁ = 1.3495863840638673
│   β₂ = 1.3521901674991565
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.748967636133747e-6 from total weight 2.007126065968527: operator might not be hermitian?
│   α = 0.7855947486826597 + 1.748967636133747e-6im
│   β₁ = 1.3521901674991565
│   β₂ = 1.2581644115329562
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.8063431283139864e-6 from total weight 1.9589927438694472: operator might not be hermitian?
│   α = 0.8791231530779282 + 1.8063431283139864e-6im
│   β₁ = 1.2581644115329562
│   β₂ = 1.2172992096457365
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.5885285506861413e-6 from total weight 1.9829497440587416: operator might not be hermitian?
│   α = 0.9043769872180605 + 1.5885285506861413e-6im
│   β₁ = 1.2172992096457365
│   β₂ = 1.2776441549376552
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.5188320461479582e-6 from total weight 1.9588640484991768: operator might not be hermitian?
│   α = 0.6899280363007593 + 1.5188320461479582e-6im
│   β₁ = 1.2776441549376552
│   β₂ = 1.3148281555321597
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.8580505688672172e-6 from total weight 2.008682608503421: operator might not be hermitian?
│   α = 0.6913519715595543 + 1.8580505688672172e-6im
│   β₁ = 1.3148281555321597
│   β₂ = 1.3520596120516548
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.956068479325515e-6 from total weight 1.9935567596530768: operator might not be hermitian?
│   α = 0.6475058176538288 + 1.956068479325515e-6im
│   β₁ = 1.3520596120516548
│   β₂ = 1.314130729995241
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.9744130875937183e-6 from total weight 2.0021703956141623: operator might not be hermitian?
│   α = 0.782921176999384 + 1.9744130875937183e-6im
│   β₁ = 1.314130729995241
│   β₂ = 1.2918131243171154
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6117145099628014e-6 from total weight 2.0198779920499415: operator might not be hermitian?
│   α = 0.7898358256992374 + 1.6117145099628014e-6im
│   β₁ = 1.2918131243171154
│   β₂ = 1.3368939086738196
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3593759494220231e-6 from total weight 2.019513392870969: operator might not be hermitian?
│   α = 0.7955165842907529 + 1.3593759494220231e-6im
│   β₁ = 1.3368939086738196
│   β₂ = 1.2877509017867448
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0936758011396291e-6 from total weight 1.962446160174074: operator might not be hermitian?
│   α = 0.7681454973098479 + 1.0936758011396291e-6im
│   β₁ = 1.0473109475340552
│   β₂ = 1.4711516596594305
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.4140393918386784e-6 from total weight 2.3305892057232325: operator might not be hermitian?
│   α = 1.2725888691538776 + 1.4140393918386784e-6im
│   β₁ = 1.4711516596594305
│   β₂ = 1.2836963855283718
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2363655292799668e-6 from total weight 1.9215446561532274: operator might not be hermitian?
│   α = 0.7043198883856858 + 1.2363655292799668e-6im
│   β₁ = 1.2836963855283718
│   β₂ = 1.2443435820525077
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3621234929601933e-6 from total weight 2.031241267058665: operator might not be hermitian?
│   α = 0.8491909978696255 + 1.3621234929601933e-6im
│   β₁ = 1.2443435820525077
│   β₂ = 1.362506801429688
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.5702297864253478e-6 from total weight 2.0046033526873535: operator might not be hermitian?
│   α = 0.6551477286897311 + 1.5702297864253478e-6im
│   β₁ = 1.362506801429688
│   β₂ = 1.3163552982585813
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.5972965097966335e-6 from total weight 1.9982889168855587: operator might not be hermitian?
│   α = 0.6762387934135368 + 1.5972965097966335e-6im
│   β₁ = 1.3163552982585813
│   β₂ = 1.3427838315880456
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.5781264739826717e-6 from total weight 2.0091768575110542: operator might not be hermitian?
│   α = 0.797943851228216 + 1.5781264739826717e-6im
│   β₁ = 1.3427838315880456
│   β₂ = 1.2637281498282438
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.500389786990644e-6 from total weight 1.9365460830408492: operator might not be hermitian?
│   α = 0.8370715044470002 + 1.500389786990644e-6im
│   β₁ = 1.2637281498282438
│   β₂ = 1.2052025520687897
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6848371347591429e-6 from total weight 1.9701367571309558: operator might not be hermitian?
│   α = 0.9381977580271958 + 1.6848371347591429e-6im
│   β₁ = 1.2052025520687897
│   β₂ = 1.2444720234361477
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.301224902904019e-6 from total weight 2.032783165297502: operator might not be hermitian?
│   α = 1.0018865864506536 + 1.301224902904019e-6im
│   β₁ = 1.3560745448480025
│   β₂ = 1.135558230044051
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.4331223396387566e-6 from total weight 1.891875931072235: operator might not be hermitian?
│   α = 0.9245962509023617 + 1.4331223396387566e-6im
│   β₁ = 1.135558230044051
│   β₂ = 1.1978413156862229
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2020958610227395e-6 from total weight 1.8535112515440146: operator might not be hermitian?
│   α = 0.7599300178221852 + 1.2020958610227395e-6im
│   β₁ = 1.1978413156862229
│   β₂ = 1.1929738094554658
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2029225218155096e-6 from total weight 1.8361265730664569: operator might not be hermitian?
│   α = 0.8126705814608668 + 1.2029225218155096e-6im
│   β₁ = 1.1929738094554658
│   β₂ = 1.1347866796454273
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.72781939736244e-6 from total weight 1.8379544196724218: operator might not be hermitian?
│   α = 0.7746976579831134 + 1.72781939736244e-6im
│   β₁ = 1.1347866796454273
│   β₂ = 1.220728954029185
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3164896480177823e-6 from total weight 1.8641899207308146: operator might not be hermitian?
│   α = 0.753715042628617 + 1.3164896480177823e-6im
│   β₁ = 1.220728954029185
│   β₂ = 1.1903522654503504
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.1951999317263984e-6 from total weight 1.8262076303378614: operator might not be hermitian?
│   α = 0.7790016654288074 + 1.1951999317263984e-6im
│   β₁ = 1.1903522654503504
│   β₂ = 1.1450992090204066
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.329043586510703e-6 from total weight 1.8656619514160093: operator might not be hermitian?
│   α = 0.8930858144233594 + 1.329043586510703e-6im
│   β₁ = 1.1450992090204066
│   β₂ = 1.1712557562446508
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.137416697809951e-6 from total weight 1.9324138401886977: operator might not be hermitian?
│   α = 0.8059601405207465 + 1.137416697809951e-6im
│   β₁ = 1.1712557562446508
│   β₂ = 1.3087442282994357
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2041512158535161e-6 from total weight 1.8635788832563664: operator might not be hermitian?
│   α = 0.624787036120966 + 1.2041512158535161e-6im
│   β₁ = 1.3087442282994357
│   β₂ = 1.170365737069267
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6380061677104263e-6 from total weight 1.79911763127121: operator might not be hermitian?
│   α = 0.8545636636861133 + 1.6380061677104263e-6im
│   β₁ = 1.170365737069267
│   β₂ = 1.0662031876476101
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2228514773388825e-6 from total weight 1.8124365450754356: operator might not be hermitian?
│   α = 0.9939764795428676 + 1.2228514773388825e-6im
│   β₁ = 1.0662031876476101
│   β₂ = 1.0771015507783512
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3577038761106164e-6 from total weight 1.7818490802101545: operator might not be hermitian?
│   α = 0.8828101046503334 + 1.3577038761106164e-6im
│   β₁ = 1.0771015507783512
│   β₂ = 1.1115235998763446
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.573225774296333e-6 from total weight 1.7952965109074976: operator might not be hermitian?
│   α = 0.8037556413672008 + 1.573225774296333e-6im
│   β₁ = 1.1115235998763446
│   β₂ = 1.1582666868914475
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.9993628590166297e-6 from total weight 1.7966684663477028: operator might not be hermitian?
│   α = 0.7833344237000951 + 1.9993628590166297e-6im
│   β₁ = 1.1582666868914475
│   β₂ = 1.1281945934315403
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.4402545049987947e-6 from total weight 1.7911396609775052: operator might not be hermitian?
│   α = 0.8380019083518554 + 1.4402545049987947e-6im
│   β₁ = 1.1281945934315403
│   β₂ = 1.110455332768963
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.2109032088564176e-6 from total weight 1.7813199833273619: operator might not be hermitian?
│   α = 0.7777249070445168 + 1.2109032088564176e-6im
│   β₁ = 1.110455332768963
│   β₂ = 1.1554799028488103
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.36909457887531e-6 from total weight 1.7554473671236752: operator might not be hermitian?
│   α = 0.7782114591736479 + 1.36909457887531e-6im
│   β₁ = 1.1554799028488103
│   β₂ = 1.0681051341805705
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6953973636414654e-6 from total weight 1.8478627263512848: operator might not be hermitian?
│   α = 1.0786054983876303 + 1.6953973636414654e-6im
│   β₁ = 1.0681051341805705
│   β₂ = 1.0537353826367444
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.757283796120085e-6 from total weight 1.8111473736314618: operator might not be hermitian?
│   α = 0.9110031771776171 + 1.757283796120085e-6im
│   β₁ = 1.0537353826367444
│   β₂ = 1.1575706300527562
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6318890057095276e-6 from total weight 1.8203681556361564: operator might not be hermitian?
│   α = 0.9124447934701678 + 1.6318890057095276e-6im
│   β₁ = 1.1575706300527562
│   β₂ = 1.0682766296048822
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.8390788291272608e-6 from total weight 1.742392537575849: operator might not be hermitian?
│   α = 0.8617339094018543 + 1.8390788291272608e-6im
│   β₁ = 1.0682766296048822
│   β₂ = 1.0733738710363945
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6564830520246487e-6 from total weight 1.7426059463027106: operator might not be hermitian?
│   α = 0.7671804483853782 + 1.6564830520246487e-6im
│   β₁ = 1.0733738710363945
│   β₂ = 1.138410372703261
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.852045748698336e-6 from total weight 1.8175974775984134: operator might not be hermitian?
│   α = 0.7528916040098729 + 1.852045748698336e-6im
│   β₁ = 1.138410372703261
│   β₂ = 1.2003485520888286
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.6617520472352737e-6 from total weight 1.8926943344910268: operator might not be hermitian?
│   α = 0.8539520758169454 + 1.6617520472352737e-6im
│   β₁ = 1.2003485520888286
│   β₂ = 1.1883690712560016
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3522051637501753e-6 from total weight 1.8705455442967294: operator might not be hermitian?
│   α = 0.9282228149268801 + 1.3522051637501753e-6im
│   β₁ = 1.1883690712560016
│   β₂ = 1.1068522889789256
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0122348380516705e-6 from total weight 1.7670985003089827: operator might not be hermitian?
│   α = 0.930628231856587 + 1.0122348380516705e-6im
│   β₁ = 1.1068522889789256
│   β₂ = 1.0156014052012858
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.3856631444933258e-6 from total weight 1.825912721996031: operator might not be hermitian?
│   α = 1.0815656907671525 + 1.3856631444933258e-6im
│   β₁ = 1.0156014052012858
│   β₂ = 1.0642963453162757
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS   3:	obj = -2.945462988948e-01	err = 3.4609424308e-01	time = 0.03 sec
┌ Warning: ignoring imaginary component -1.392483040988518e-6 from total weight 1.8955122145817562: operator might not be hermitian?
│   α = 1.101941371687926 - 1.392483040988518e-6im
│   β₁ = 1.0798020846906913
│   β₂ = 1.1012353185794865
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0753622344539249e-6 from total weight 1.8648990216541668: operator might not be hermitian?
│   α = 0.8383791538157135 - 1.0753622344539249e-6im
│   β₁ = 1.1012353185794865
│   β₂ = 1.2498998073949357
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2549910538232206e-6 from total weight 2.1121408373175985: operator might not be hermitian?
│   α = 1.3409655729255554 - 1.2549910538232206e-6im
│   β₁ = 1.2136080492246442
│   β₂ = 1.0909196816212923
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.4022760645906324e-6 from total weight 1.7304296250907174: operator might not be hermitian?
│   α = 0.8127621709548318 - 1.4022760645906324e-6im
│   β₁ = 1.0909196816212923
│   β₂ = 1.0694384456833976
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.4313764805165552e-6 from total weight 1.8794569157231034: operator might not be hermitian?
│   α = 1.0784242798463932 - 1.4313764805165552e-6im
│   β₁ = 1.0694384456833976
│   β₂ = 1.1070956515086754
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1180232882476715e-6 from total weight 1.8844800254598146: operator might not be hermitian?
│   α = 1.216318455706141 - 1.1180232882476715e-6im
│   β₁ = 1.0649907248461274
│   β₂ = 0.9683125201380608
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS   4:	obj = -2.319707042439e-01	err = 3.6024027466e-01	time = 0.02 sec
┌ Warning: ignoring imaginary component -1.0204260968149637e-6 from total weight 1.7960622649204319: operator might not be hermitian?
│   α = 0.8465484658404078 - 1.0204260968149637e-6im
│   β₁ = 1.0893153937710733
│   β₂ = 1.1500379677848442
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -9.980297221391307e-7 from total weight 1.724221091947597: operator might not be hermitian?
│   α = 0.6903523472065521 - 9.980297221391307e-7im
│   β₁ = 1.1477237120574055
│   β₂ = 1.0858555573387934
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS   5:	obj = -3.341745290133e-01	err = 3.3118494023e-01	time = 0.08 sec
[ Info: VUMPS   6:	obj = -3.494924855347e-01	err = 2.8628386188e-01	time = 0.03 sec
┌ Warning: ignoring imaginary component -1.2137926916363064e-6 from total weight 1.8486757461171281: operator might not be hermitian?
│   α = 0.771117205144365 - 1.2137926916363064e-6im
│   β₁ = 1.1911622391957852
│   β₂ = 1.1849526531151673
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8052469317100112e-6 from total weight 1.8549819756331998: operator might not be hermitian?
│   α = 0.8368904023840432 - 1.8052469317100112e-6im
│   β₁ = 1.1849526531151673
│   β₂ = 1.1560535429613934
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.0673666736130414e-6 from total weight 1.879996592383449: operator might not be hermitian?
│   α = 0.882809938116432 - 2.0673666736130414e-6im
│   β₁ = 1.1560535429613934
│   β₂ = 1.1910390448420975
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.194385859464673e-6 from total weight 1.7942145377417382: operator might not be hermitian?
│   α = 0.8003805303951113 - 2.194385859464673e-6im
│   β₁ = 1.1910390448420975
│   β₂ = 1.0770435495675412
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.3709987418962797e-6 from total weight 1.8718062529591089: operator might not be hermitian?
│   α = 0.956423888603269 - 2.3709987418962797e-6im
│   β₁ = 1.0770435495675412
│   β₂ = 1.19536152951948
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.3673814470905746e-6 from total weight 1.8555379367315137: operator might not be hermitian?
│   α = 0.8933821221410543 - 2.3673814470905746e-6im
│   β₁ = 1.19536152951948
│   β₂ = 1.102724005464574
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.334346772072532e-6 from total weight 1.888065121940592: operator might not be hermitian?
│   α = 0.9721742902891686 - 2.334346772072532e-6im
│   β₁ = 1.102724005464574
│   β₂ = 1.1847644583443624
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.177633131844603e-6 from total weight 1.9390501291320332: operator might not be hermitian?
│   α = 1.014147105401859 - 2.177633131844603e-6im
│   β₁ = 1.1847644583443624
│   β₂ = 1.152282183378374
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9774983512077515e-6 from total weight 1.8305152178308537: operator might not be hermitian?
│   α = 0.7177922188043688 - 1.9774983512077515e-6im
│   β₁ = 1.152282183378374
│   β₂ = 1.2279275480251655
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9651366731853956e-6 from total weight 1.8439158098506916: operator might not be hermitian?
│   α = 0.6857331180630781 - 1.9651366731853956e-6im
│   β₁ = 1.2279275480251655
│   β₂ = 1.1924720296115392
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.0190197140557142e-6 from total weight 1.8592053567515292: operator might not be hermitian?
│   α = 0.7838374650404871 - 2.0190197140557142e-6im
│   β₁ = 1.1924720296115392
│   β₂ = 1.1917440352536046
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.105103661853916e-6 from total weight 1.8407455207629144: operator might not be hermitian?
│   α = 0.840354593043139 - 2.105103661853916e-6im
│   β₁ = 1.1917440352536046
│   β₂ = 1.1233407250665566
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.06494826259819e-6 from total weight 1.841267305393983: operator might not be hermitian?
│   α = 0.8882808636031334 - 2.06494826259819e-6im
│   β₁ = 1.1233407250665566
│   β₂ = 1.15729339956295
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.2230019045606925e-6 from total weight 1.8228821941757196: operator might not be hermitian?
│   α = 0.7940779018084841 - 2.2230019045606925e-6im
│   β₁ = 1.15729339956295
│   β₂ = 1.1631903399811268
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.145042114523512e-6 from total weight 1.8171564444253046: operator might not be hermitian?
│   α = 0.8544521983500817 - 2.145042114523512e-6im
│   β₁ = 1.1631903399811268
│   β₂ = 1.104063955222304
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.6467638147572156e-6 from total weight 1.8097942535063836: operator might not be hermitian?
│   α = 0.8187040301882722 - 1.6467638147572156e-6im
│   β₁ = 1.104063955222304
│   β₂ = 1.177336712140745
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.5244830939625462e-6 from total weight 1.8186387999784603: operator might not be hermitian?
│   α = 0.6481570111134087 - 1.5244830939625462e-6im
│   β₁ = 1.177336712140745
│   β₂ = 1.2252419516058546
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9022438640223151e-6 from total weight 1.845672069956571: operator might not be hermitian?
│   α = 0.8341584370695838 - 1.9022438640223151e-6im
│   β₁ = 1.2252419516058546
│   β₂ = 1.0997578150233172
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.097853804325367e-6 from total weight 1.859100484948138: operator might not be hermitian?
│   α = 0.9829316071898353 - 2.097853804325367e-6im
│   β₁ = 1.0997578150233172
│   β₂ = 1.1316504835912666
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.218477325925325e-6 from total weight 1.824760097059155: operator might not be hermitian?
│   α = 0.7981966528552535 - 2.218477325925325e-6im
│   β₁ = 1.1316504835912666
│   β₂ = 1.1882755144211035
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.107775001676873e-6 from total weight 1.7948760632162533: operator might not be hermitian?
│   α = 0.715662975666142 - 2.107775001676873e-6im
│   β₁ = 1.1882755144211035
│   β₂ = 1.1390381422016462
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8943371334406364e-6 from total weight 1.7786107483977287: operator might not be hermitian?
│   α = 0.7939679645380324 - 1.8943371334406364e-6im
│   β₁ = 1.1390381422016462
│   β₂ = 1.111603875582258
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.940765476975831e-6 from total weight 1.8050001473989414: operator might not be hermitian?
│   α = 0.8874112102188971 - 1.940765476975831e-6im
│   β₁ = 1.111603875582258
│   β₂ = 1.111244212527008
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.199444159377284e-6 from total weight 1.759110189883705: operator might not be hermitian?
│   α = 0.8304008173000483 - 2.199444159377284e-6im
│   β₁ = 1.111244212527008
│   β₂ = 1.081683614972737
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.404082553034842e-6 from total weight 1.7701574894902945: operator might not be hermitian?
│   α = 0.8176565476152748 - 2.404082553034842e-6im
│   β₁ = 1.081683614972737
│   β₂ = 1.1379173365557727
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.1608698665687154e-6 from total weight 1.777911385657947: operator might not be hermitian?
│   α = 0.702221919442864 - 2.1608698665687154e-6im
│   β₁ = 1.1379173365557727
│   β₂ = 1.1717497199774738
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.0444276374407405e-6 from total weight 1.8530092878500277: operator might not be hermitian?
│   α = 0.9004041535488609 - 2.0444276374407405e-6im
│   β₁ = 1.1717497199774738
│   β₂ = 1.1179974842811402
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.2029817202846858e-6 from total weight 1.8209273687022072: operator might not be hermitian?
│   α = 0.8967101105620928 - 2.2029817202846858e-6im
│   β₁ = 0.8788405586960297
│   β₂ = 1.3188353695933623
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.216417890362702e-6 from total weight 2.1106092940068626: operator might not be hermitian?
│   α = 1.2231888468396814 - 2.216417890362702e-6im
│   β₁ = 1.3188353695933623
│   β₂ = 1.104153025997658
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.3737135441750934e-6 from total weight 1.7108761064821731: operator might not be hermitian?
│   α = 0.7689084483760471 - 2.3737135441750934e-6im
│   β₁ = 1.104153025997658
│   β₂ = 1.056751127239579
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.2950472934567256e-6 from total weight 1.805845919611404: operator might not be hermitian?
│   α = 0.9011490916083735 - 2.2950472934567256e-6im
│   β₁ = 1.056751127239579
│   β₂ = 1.1542473110833626
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9165190242613137e-6 from total weight 1.7806954185448687: operator might not be hermitian?
│   α = 0.6766133971213509 - 1.9165190242613137e-6im
│   β₁ = 1.1542473110833626
│   β₂ = 1.175067499897663
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7371752475472957e-6 from total weight 1.7997772548877546: operator might not be hermitian?
│   α = 0.682777908206393 - 1.7371752475472957e-6im
│   β₁ = 1.175067499897663
│   β₂ = 1.1799274833471092
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9827521738555176e-6 from total weight 1.826349907461843: operator might not be hermitian?
│   α = 0.8580873616013737 - 1.9827521738555176e-6im
│   β₁ = 1.1799274833471092
│   β₂ = 1.0986406138424443
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.91092151146776e-6 from total weight 1.7435181739830286: operator might not be hermitian?
│   α = 0.7394903063302251 - 1.91092151146776e-6im
│   β₁ = 1.0986406138424443
│   β₂ = 1.134018743877274
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9595898916001386e-6 from total weight 1.8251022615462704: operator might not be hermitian?
│   α = 0.9164809096157032 - 1.9595898916001386e-6im
│   β₁ = 1.134018743877274
│   β₂ = 1.0977533857576816
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.05986185874453e-6 from total weight 1.8186394706547202: operator might not be hermitian?
│   α = 0.9455626165039587 - 2.05986185874453e-6im
│   β₁ = 1.0977533857576816
│   β₂ = 1.0992262581228545
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9751055681822144e-6 from total weight 1.8210053523773804: operator might not be hermitian?
│   α = 0.9358713510025474 - 1.9751055681822144e-6im
│   β₁ = 1.0992262581228545
│   β₂ = 1.1099130331737983
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.982306293563628e-6 from total weight 1.7917057681901003: operator might not be hermitian?
│   α = 0.9121882545888488 - 1.982306293563628e-6im
│   β₁ = 1.1099130331737983
│   β₂ = 1.0706144061905936
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.196445485691187e-6 from total weight 1.7744014664512398: operator might not be hermitian?
│   α = 0.874804800955041 - 2.196445485691187e-6im
│   β₁ = 0.5978282520080367
│   β₂ = 1.4233125115260221
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.180456329423097e-6 from total weight 2.1061953707531647: operator might not be hermitian?
│   α = 1.1540327503490424 - 2.180456329423097e-6im
│   β₁ = 1.4233125115260221
│   β₂ = 1.0384839167905384
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.151285085509602e-6 from total weight 1.804623532007284: operator might not be hermitian?
│   α = 0.8516682302055673 - 2.151285085509602e-6im
│   β₁ = 1.0384839167905384
│   β₂ = 1.2053540859414364
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9497181986960488e-6 from total weight 1.8272748413277866: operator might not be hermitian?
│   α = 0.7717001680448697 - 1.9497181986960488e-6im
│   β₁ = 1.2053540859414364
│   β₂ = 1.1360166037032604
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9811992536446915e-6 from total weight 1.8330648060187416: operator might not be hermitian?
│   α = 0.9324764918655245 - 1.9811992536446915e-6im
│   β₁ = 1.1360166037032604
│   β₂ = 1.0954818352164835
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.444192831056429e-6 from total weight 1.680031417900311: operator might not be hermitian?
│   α = 0.8412545867799889 - 1.444192831056429e-6im
│   β₁ = 1.0396167334930557
│   β₂ = 1.0168546271679657
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.012070060116583e-6 from total weight 1.6996488398921563: operator might not be hermitian?
│   α = 0.9563600153628701 - 2.012070060116583e-6im
│   β₁ = 1.0168546271679657
│   β₂ = 0.969633109565124
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.2284985421137937e-6 from total weight 1.625611124450328: operator might not be hermitian?
│   α = 0.9076143355875635 - 2.2284985421137937e-6im
│   β₁ = 0.969633109565124
│   β₂ = 0.9373683260078226
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.3787217767051727e-6 from total weight 1.6320977987504197: operator might not be hermitian?
│   α = 0.9151559473878687 - 2.3787217767051727e-6im
│   β₁ = 0.9373683260078226
│   β₂ = 0.9734338385520672
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.4459831018432132e-6 from total weight 1.7171504373726327: operator might not be hermitian?
│   α = 1.0490080777046167 - 2.4459831018432132e-6im
│   β₁ = 0.9734338385520672
│   β₂ = 0.949006975440799
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.502042695789325e-6 from total weight 1.7461038387840222: operator might not be hermitian?
│   α = 1.063200920663453 - 2.502042695789325e-6im
│   β₁ = 0.949006975440799
│   β₂ = 1.0088945329791073
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.2991596320565827e-6 from total weight 1.7649566358660225: operator might not be hermitian?
│   α = 1.0323010887631134 - 2.2991596320565827e-6im
│   β₁ = 1.0088945329791073
│   β₂ = 1.0156565413295877
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.3680517285112196e-6 from total weight 1.6911743091363975: operator might not be hermitian?
│   α = 0.822688208588965 - 2.3680517285112196e-6im
│   β₁ = 1.0156565413295877
│   β₂ = 1.0731712097239952
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.3240639867236346e-6 from total weight 1.7008433430515881: operator might not be hermitian?
│   α = 0.9047109560948917 - 2.3240639867236346e-6im
│   β₁ = 1.0731712097239952
│   β₂ = 0.96055698328569
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.4438641293214602e-6 from total weight 1.6863390242825544: operator might not be hermitian?
│   α = 1.0018650093118424 - 2.4438641293214602e-6im
│   β₁ = 0.96055698328569
│   β₂ = 0.9577766387785523
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.2852982025176743e-6 from total weight 1.6664847188204572: operator might not be hermitian?
│   α = 0.9481338905918142 - 2.2852982025176743e-6im
│   β₁ = 0.9577766387785523
│   β₂ = 0.980243517590483
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.6503217592163675e-6 from total weight 1.6570209299072616: operator might not be hermitian?
│   α = 0.9553022495142013 - 2.6503217592163675e-6im
│   β₁ = 0.980243517590483
│   β₂ = 0.9339371608618243
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.4977568402820283e-6 from total weight 1.6146874716863424: operator might not be hermitian?
│   α = 0.9937470670638898 - 2.4977568402820283e-6im
│   β₁ = 0.9339371608618243
│   β₂ = 0.8645483083540594
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7911041787048443e-6 from total weight 1.6526314248172924: operator might not be hermitian?
│   α = 0.9942222833655865 - 1.7911041787048443e-6im
│   β₁ = 0.8645483083540594
│   β₂ = 0.997631645484384
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0910619358400764e-6 from total weight 1.628256128074027: operator might not be hermitian?
│   α = 0.7468594858110634 - 1.0910619358400764e-6im
│   β₁ = 0.997631645484384
│   β₂ = 1.047926537020409
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.4086345025538481e-6 from total weight 1.7208828389475097: operator might not be hermitian?
│   α = 1.0230379305064004 - 1.4086345025538481e-6im
│   β₁ = 1.047926537020409
│   β₂ = 0.9037041059637005
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.5801647672217256e-6 from total weight 1.6935875767437443: operator might not be hermitian?
│   α = 1.0573393121341177 - 1.5801647672217256e-6im
│   β₁ = 0.9037041059637005
│   β₂ = 0.966225309117056
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8503500605684953e-6 from total weight 1.687885653739837: operator might not be hermitian?
│   α = 0.9077058420558016 - 1.8503500605684953e-6im
│   β₁ = 0.966225309117056
│   β₂ = 1.0447184962547331
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7245869534127795e-6 from total weight 1.630010231135931: operator might not be hermitian?
│   α = 0.8428816315538215 - 1.7245869534127795e-6im
│   β₁ = 1.0447184962547331
│   β₂ = 0.9246876079937777
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.669866318011401e-6 from total weight 1.5672706436085126: operator might not be hermitian?
│   α = 0.7835317567308676 - 1.669866318011401e-6im
│   β₁ = 0.9246876079937777
│   β₂ = 0.9936639694238888
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7442226515947817e-6 from total weight 1.6505309294564066: operator might not be hermitian?
│   α = 0.8815928759787162 - 1.7442226515947817e-6im
│   β₁ = 0.9936639694238888
│   β₂ = 0.9796316991510248
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.5551504819709405e-6 from total weight 1.6065777130754422: operator might not be hermitian?
│   α = 0.7930473224308218 - 1.5551504819709405e-6im
│   β₁ = 0.9796316991510248
│   β₂ = 0.9962377359606892
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.5768281077382929e-6 from total weight 1.6432036667533771: operator might not be hermitian?
│   α = 0.8513104308677694 - 1.5768281077382929e-6im
│   β₁ = 0.9962377359606892
│   β₂ = 0.9914127365395857
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7341376412037535e-6 from total weight 1.6510721319879114: operator might not be hermitian?
│   α = 0.9480572889512263 - 1.7341376412037535e-6im
│   β₁ = 0.9914127365395857
│   β₂ = 0.9188728680931008
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.0380127565208794e-6 from total weight 1.6657878517427898: operator might not be hermitian?
│   α = 1.0551087967110504 - 2.0380127565208794e-6im
│   β₁ = 0.9188728680931008
│   β₂ = 0.9040283438006927
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9689745632016017e-6 from total weight 1.6316000751641972: operator might not be hermitian?
│   α = 1.0068062496864232 - 1.9689745632016017e-6im
│   β₁ = 0.9040283438006927
│   β₂ = 0.9116977209959855
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7641602776535814e-6 from total weight 1.643619185973048: operator might not be hermitian?
│   α = 0.9832497995595976 - 1.7641602776535814e-6im
│   β₁ = 0.9116977209959855
│   β₂ = 0.9505320224444467
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8717770270057499e-6 from total weight 1.6186044448934445: operator might not be hermitian?
│   α = 0.933889625841253 - 1.8717770270057499e-6im
│   β₁ = 0.7782860350350426
│   β₂ = 1.0686446385215385
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9087480197105267e-6 from total weight 1.872223188302107: operator might not be hermitian?
│   α = 1.1855968939468708 - 1.9087480197105267e-6im
│   β₁ = 1.0686446385215385
│   β₂ = 0.9785593024621279
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.9402894978638036e-6 from total weight 1.565662888890479: operator might not be hermitian?
│   α = 0.8073816698233107 - 1.9402894978638036e-6im
│   β₁ = 0.9785593024621279
│   β₂ = 0.9175275540512514
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.911761391519551e-6 from total weight 1.69861571249875: operator might not be hermitian?
│   α = 0.9952744384587691 - 1.911761391519551e-6im
│   β₁ = 0.9175275540512514
│   β₂ = 1.0260932308768491
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8291039981729873e-6 from total weight 1.6498451539412835: operator might not be hermitian?
│   α = 0.858745751697278 - 1.8291039981729873e-6im
│   β₁ = 1.0260932308768491
│   β₂ = 0.9652344002732076
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.1171286886112473e-6 from total weight 1.6049927885630448: operator might not be hermitian?
│   α = 0.9039923380658194 - 2.1171286886112473e-6im
│   β₁ = 0.9652344002732076
│   β₂ = 0.9094626196729643
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7631975034633485e-6 from total weight 1.6635044587627164: operator might not be hermitian?
│   α = 1.0268033716558147 - 1.7631975034633485e-6im
│   β₁ = 0.9094626196729643
│   β₂ = 0.9411693066043798
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.7538638426399522e-6 from total weight 1.598357955260205: operator might not be hermitian?
│   α = 0.8395676881149241 - 1.7538638426399522e-6im
│   β₁ = 0.9411693066043798
│   β₂ = 0.9818729991804948
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.466572661972844e-6 from total weight 1.6275090983582583: operator might not be hermitian?
│   α = 0.8477297716903176 - 1.466572661972844e-6im
│   β₁ = 0.9818729991804948
│   β₂ = 0.9828863173871848
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2983254894863294e-6 from total weight 1.6025938022231123: operator might not be hermitian?
│   α = 0.8238345469560299 - 1.2983254894863294e-6im
│   β₁ = 0.9828863173871848
│   β₂ = 0.961008855972232
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.753803488737521e-6 from total weight 1.6853450238186074: operator might not be hermitian?
│   α = 1.0058728121272003 - 1.753803488737521e-6im
│   β₁ = 0.961008855972232
│   β₂ = 0.9513515196147673
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8713013819338098e-6 from total weight 1.6457558464254889: operator might not be hermitian?
│   α = 0.953253090989849 - 1.8713013819338098e-6im
│   β₁ = 0.9513515196147673
│   β₂ = 0.945912858927897
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.1940684603594107e-6 from total weight 1.6685947310681075: operator might not be hermitian?
│   α = 1.0035877974418752 - 2.1940684603594107e-6im
│   β₁ = 0.5519727146275405
│   β₂ = 1.2134026667499564
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -2.0196296084545873e-6 from total weight 1.9239962959657293: operator might not be hermitian?
│   α = 1.2417813732350762 - 2.0196296084545873e-6im
│   β₁ = 1.2134026667499564
│   β₂ = 0.8290927187572397
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8201529821404439e-6 from total weight 1.6421902342159629: operator might not be hermitian?
│   α = 1.1015110960833447 - 1.8201529821404439e-6im
│   β₁ = 0.8290927187572397
│   β₂ = 0.8922260555823076
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.8864060040545833e-6 from total weight 1.6289668855724284: operator might not be hermitian?
│   α = 1.054375019166633 - 1.8864060040545833e-6im
│   β₁ = 0.8922260555823076
│   β₂ = 0.8635734473600828
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS   7:	obj = -2.477828349789e-01	err = 3.6861869835e-01	time = 0.04 sec
┌ Warning: ignoring imaginary component 9.797819969445398e-7 from total weight 1.7826507126092328: operator might not be hermitian?
│   α = 0.37266497932262266 + 9.797819969445398e-7im
│   β₁ = 1.2529923849189937
│   β₂ = 1.2120125658122227
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0083546393710799e-6 from total weight 1.5121046107716045: operator might not be hermitian?
│   α = 0.42712182311279506 + 1.0083546393710799e-6im
│   β₁ = 1.0452302250562036
│   β₂ = 1.0057440423713626
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 8.626484624303654e-7 from total weight 1.5025688882814423: operator might not be hermitian?
│   α = 0.3906593447423297 + 8.626484624303654e-7im
│   β₁ = 0.8502359245275253
│   β₂ = 1.175668921524637
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS   8:	obj = +3.021742828810e-02	err = 3.8513237752e-01	time = 0.02 sec
[ Info: VUMPS   9:	obj = -8.745011232470e-02	err = 3.9063780450e-01	time = 0.02 sec
[ Info: VUMPS  10:	obj = -1.499513490072e-01	err = 3.7840293472e-01	time = 0.06 sec
[ Info: VUMPS  11:	obj = -2.958681759723e-01	err = 3.3123568953e-01	time = 0.03 sec
[ Info: VUMPS  12:	obj = -7.976662855182e-03	err = 3.9656031279e-01	time = 0.03 sec
[ Info: VUMPS  13:	obj = -5.967400377513e-02	err = 3.9708070211e-01	time = 0.03 sec
[ Info: VUMPS  14:	obj = -1.005858342981e-01	err = 3.6761593768e-01	time = 0.02 sec
┌ Warning: ignoring imaginary component 1.1228371103039203e-6 from total weight 1.925618999181602: operator might not be hermitian?
│   α = 0.3165350873163584 + 1.1228371103039203e-6im
│   β₁ = 1.326599888107445
│   β₂ = 1.359392071986163
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0111171559745724e-6 from total weight 1.7301725734241629: operator might not be hermitian?
│   α = 0.3705094109208439 + 1.0111171559745724e-6im
│   β₁ = 1.2507643011136502
│   β₂ = 1.136577570299071
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0452915227276982e-6 from total weight 1.7398003898725583: operator might not be hermitian?
│   α = 0.32520104482655454 + 1.0452915227276982e-6im
│   β₁ = 1.136577570299071
│   β₂ = 1.276456463705829
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.043670650770212e-6 from total weight 1.741533774893118: operator might not be hermitian?
│   α = 0.230415239863528 + 1.043670650770212e-6im
│   β₁ = 1.225976649377648
│   β₂ = 1.2152489298541975
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 9.49492928604273e-7 from total weight 1.7203306219892969: operator might not be hermitian?
│   α = 0.28756839381882887 + 9.49492928604273e-7im
│   β₁ = 1.2152489298541975
│   β₂ = 1.1832209879468272
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0232852264632775e-6 from total weight 1.686947657369024: operator might not be hermitian?
│   α = 0.22818200575305508 + 1.0232852264632775e-6im
│   β₁ = 1.16015510353531
│   β₂ = 1.2032312773084308
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 9.778034893506704e-7 from total weight 1.7441005741153381: operator might not be hermitian?
│   α = 0.3359468737393356 + 9.778034893506704e-7im
│   β₁ = 1.2032312773084308
│   β₂ = 1.2170706651464347
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 9.625125309067895e-7 from total weight 1.6930493324860827: operator might not be hermitian?
│   α = 0.15689474930621 + 9.625125309067895e-7im
│   β₁ = 1.2170706651464347
│   β₂ = 1.1664214829600834
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0255041846228552e-6 from total weight 1.6163568378358877: operator might not be hermitian?
│   α = 0.15946995305765732 + 1.0255041846228552e-6im
│   β₁ = 1.1664214829600834
│   β₂ = 1.1075376677019915
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 9.450003205895008e-7 from total weight 1.63310722976173: operator might not be hermitian?
│   α = 0.4164024184737056 + 9.450003205895008e-7im
│   β₁ = 1.1188595855688177
│   β₂ = 1.1143614662977006
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.080879533445732e-6 from total weight 1.614688674276658: operator might not be hermitian?
│   α = 0.30429877958921225 + 1.080879533445732e-6im
│   β₁ = 1.1143614662977006
│   β₂ = 1.1281933743855694
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0988263242361906e-6 from total weight 1.6115083028404351: operator might not be hermitian?
│   α = 0.2897351912699093 + 1.0988263242361906e-6im
│   β₁ = 1.1281933743855694
│   β₂ = 1.113639187104487
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.003436960373555e-6 from total weight 1.6172105156629197: operator might not be hermitian?
│   α = 0.14272259326333872 + 1.003436960373555e-6im
│   β₁ = 1.113639187104487
│   β₂ = 1.1639621446967956
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 1.0252943553334948e-6 from total weight 1.6211799504508382: operator might not be hermitian?
│   α = 0.1247595589372499 + 1.0252943553334948e-6im
│   β₁ = 1.1829896553891046
│   β₂ = 1.10145129689827
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 9.687233263298844e-7 from total weight 1.5808042072341244: operator might not be hermitian?
│   α = 0.1804895992486852 + 9.687233263298844e-7im
│   β₁ = 1.10145129689827
│   β₂ = 1.1194509755823783
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component 9.67778768440515e-7 from total weight 1.564685677695013: operator might not be hermitian?
│   α = 0.27799810530818225 + 9.67778768440515e-7im
│   β₁ = 0.9536269829322506
│   β₂ = 1.2089474351069032
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS  15:	obj = -1.268018919710e-01	err = 3.9770372558e-01	time = 0.03 sec
[ Info: VUMPS  16:	obj = -2.089366409470e-01	err = 3.5604649696e-01	time = 0.06 sec
┌ Warning: ignoring imaginary component -1.4642964467764807e-6 from total weight 2.394006887776447: operator might not be hermitian?
│   α = 0.8242382100564384 - 1.4642964467764807e-6im
│   β₁ = 1.655282987088156
│   β₂ = 1.520506029076635
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.3983965608810323e-6 from total weight 2.298232529409139: operator might not be hermitian?
│   α = 0.9982576460523188 - 1.3983965608810323e-6im
│   β₁ = 1.520506029076635
│   β₂ = 1.4047832028010792
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2414856767097027e-6 from total weight 2.2348174847568463: operator might not be hermitian?
│   α = 0.980492672115643 - 1.2414856767097027e-6im
│   β₁ = 1.4047832028010792
│   β₂ = 1.4351402242390265
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.4617492379419977e-6 from total weight 2.20291267013881: operator might not be hermitian?
│   α = 0.9485389110548547 - 1.4617492379419977e-6im
│   β₁ = 1.4765975180930613
│   β₂ = 1.3314495619557836
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.3979009563739458e-6 from total weight 2.1101472430666828: operator might not be hermitian?
│   α = 1.0471134224194303 - 1.3979009563739458e-6im
│   β₁ = 1.3314495619557836
│   β₂ = 1.2583786918002022
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2539214374338373e-6 from total weight 2.036435547475786: operator might not be hermitian?
│   α = 0.9129612687076675 - 1.2539214374338373e-6im
│   β₁ = 1.2583786918002022
│   β₂ = 1.3153153724047817
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS  17:	obj = -2.048644413129e-01	err = 3.6617686541e-01	time = 0.03 sec
[ Info: VUMPS  18:	obj = -2.799693370510e-01	err = 3.3255889569e-01	time = 0.03 sec
[ Info: VUMPS  19:	obj = -1.753528829672e-01	err = 3.8615523295e-01	time = 0.03 sec
[ Info: VUMPS  20:	obj = +6.627601983914e-02	err = 3.7292664656e-01	time = 0.06 sec
[ Info: VUMPS  21:	obj = -2.320790738208e-01	err = 3.6756828615e-01	time = 0.03 sec
[ Info: VUMPS  22:	obj = +9.275292947159e-03	err = 4.0192510807e-01	time = 0.02 sec
[ Info: VUMPS  23:	obj = -7.298797837172e-02	err = 3.7988627737e-01	time = 0.02 sec
[ Info: VUMPS  24:	obj = -1.854126547483e-01	err = 3.6419418325e-01	time = 0.05 sec
[ Info: VUMPS  25:	obj = -3.671777760261e-01	err = 3.0812532655e-01	time = 0.03 sec
[ Info: VUMPS  26:	obj = -6.058668310156e-02	err = 3.8116081944e-01	time = 0.03 sec
[ Info: VUMPS  27:	obj = -2.015499701872e-03	err = 4.0317162622e-01	time = 0.02 sec
[ Info: VUMPS  28:	obj = -1.933169651612e-01	err = 3.8584662029e-01	time = 0.05 sec
┌ Warning: ignoring imaginary component -1.1661211199304189e-6 from total weight 1.9830955524856506: operator might not be hermitian?
│   α = 0.7062017103994722 - 1.1661211199304189e-6im
│   β₁ = 1.2975553722381348
│   β₂ = 1.322987970652728
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1145563612105502e-6 from total weight 1.9381249814965889: operator might not be hermitian?
│   α = 0.5691588295585481 - 1.1145563612105502e-6im
│   β₁ = 1.322987970652728
│   β₂ = 1.2969539313883243
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2189929755176618e-6 from total weight 2.056544867261239: operator might not be hermitian?
│   α = 0.5470064500394781 - 1.2189929755176618e-6im
│   β₁ = 1.4301041013320408
│   β₂ = 1.3729395449274322
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1440933743427778e-6 from total weight 2.0445152640029147: operator might not be hermitian?
│   α = 0.6236570359401358 - 1.1440933743427778e-6im
│   β₁ = 1.350665796986038
│   β₂ = 1.4024252105242667
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.248874490177021e-6 from total weight 2.031575324892375: operator might not be hermitian?
│   α = 0.5290086048223288 - 1.248874490177021e-6im
│   β₁ = 1.4024252105242667
│   β₂ = 1.371368559366846
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1024766432207733e-6 from total weight 2.0089343008618497: operator might not be hermitian?
│   α = 0.7138216358572168 - 1.1024766432207733e-6im
│   β₁ = 1.371368559366846
│   β₂ = 1.282818760285451
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1510270212095053e-6 from total weight 1.9537611011393712: operator might not be hermitian?
│   α = 0.6076833782060458 - 1.1510270212095053e-6im
│   β₁ = 1.282818760285451
│   β₂ = 1.342489992676217
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.224997782992704e-6 from total weight 1.9645654639590098: operator might not be hermitian?
│   α = 0.5951035704552179 - 1.224997782992704e-6im
│   β₁ = 1.342489992676217
│   β₂ = 1.305024835845909
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1876444488932714e-6 from total weight 2.0169775219024793: operator might not be hermitian?
│   α = 0.7688953944030071 - 1.1876444488932714e-6im
│   β₁ = 1.305024835845909
│   β₂ = 1.331881516558308
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1840660663932356e-6 from total weight 1.984838719137105: operator might not be hermitian?
│   α = 0.785780036375005 - 1.1840660663932356e-6im
│   β₁ = 1.331881516558308
│   β₂ = 1.2442773409771872
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.077349919163459e-6 from total weight 1.8902174931287379: operator might not be hermitian?
│   α = 0.7502244171904665 - 1.077349919163459e-6im
│   β₁ = 1.2442773409771872
│   β₂ = 1.2090737752141907
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0988026773565973e-6 from total weight 1.9119512889411112: operator might not be hermitian?
│   α = 0.6200929725096753 - 1.0988026773565973e-6im
│   β₁ = 1.2354323373196032
│   β₂ = 1.3208896156119578
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2560645931206094e-6 from total weight 1.7909478939100432: operator might not be hermitian?
│   α = 0.7333732110449686 - 1.2560645931206094e-6im
│   β₁ = 1.1135982474665187
│   β₂ = 1.1956408471026458
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1138326366866638e-6 from total weight 1.7427923996019516: operator might not be hermitian?
│   α = 0.6189073977995818 - 1.1138326366866638e-6im
│   β₁ = 1.1956408471026458
│   β₂ = 1.1066715618455663
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -9.82501486145211e-7 from total weight 1.737355447292098: operator might not be hermitian?
│   α = 0.7353320014976531 - 9.82501486145211e-7im
│   β₁ = 1.0893509501287795
│   β₂ = 1.136224143935316
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.2054549464787095e-6 from total weight 1.765964675748259: operator might not be hermitian?
│   α = 0.5948599677205233 - 1.2054549464787095e-6im
│   β₁ = 1.136224143935316
│   β₂ = 1.2139882822874353
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1910613334550207e-6 from total weight 1.7457281622540435: operator might not be hermitian?
│   α = 0.5876265067570648 - 1.1910613334550207e-6im
│   β₁ = 1.2139882822874353
│   β₂ = 1.1083746458263801
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1145402977093266e-6 from total weight 1.8228236011903869: operator might not be hermitian?
│   α = 0.7583728039666247 - 1.1145402977093266e-6im
│   β₁ = 1.1812863090759282
│   β₂ = 1.1628066164453221
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0244123553188045e-6 from total weight 1.827416176813848: operator might not be hermitian?
│   α = 0.7209367429139465 - 1.0244123553188045e-6im
│   β₁ = 1.1628066164453221
│   β₂ = 1.2114375216029523
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0686049562343147e-6 from total weight 1.8521257122682948: operator might not be hermitian?
│   α = 0.9046242484510791 - 1.0686049562343147e-6im
│   β₁ = 1.1441752673029573
│   β₂ = 1.1414410106749817
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.02064543803463e-6 from total weight 1.8303026002338043: operator might not be hermitian?
│   α = 0.8018410455211272 - 1.02064543803463e-6im
│   β₁ = 1.1414410106749817
│   β₂ = 1.1849772003243124
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1415911429371942e-6 from total weight 1.8503026810057916: operator might not be hermitian?
│   α = 0.7878644256718402 - 1.1415911429371942e-6im
│   β₁ = 1.1849772003243124
│   β₂ = 1.1826743815641958
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1470443615248238e-6 from total weight 1.8849501176514116: operator might not be hermitian?
│   α = 0.8619538770355701 - 1.1470443615248238e-6im
│   β₁ = 1.1826743815641958
│   β₂ = 1.1880041107200983
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0568060722793843e-6 from total weight 1.7864879735856112: operator might not be hermitian?
│   α = 0.7350531632675616 - 1.0568060722793843e-6im
│   β₁ = 1.1880041107200983
│   β₂ = 1.1135000493252825
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -9.602859024383792e-7 from total weight 1.7025702297398062: operator might not be hermitian?
│   α = 0.6791999518194767 - 9.602859024383792e-7im
│   β₁ = 1.1135000493252825
│   β₂ = 1.0943264836402107
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0558620769408888e-6 from total weight 1.7596527593571747: operator might not be hermitian?
│   α = 0.7769001371869034 - 1.0558620769408888e-6im
│   β₁ = 1.1619115114008967
│   β₂ = 1.0690021749394427
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.0354194948727913e-6 from total weight 1.7038410836176745: operator might not be hermitian?
│   α = 0.7165984827525741 - 1.0354194948727913e-6im
│   β₁ = 1.0690021749394427
│   β₂ = 1.116599929569149
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.091324247760525e-6 from total weight 1.7342773510387077: operator might not be hermitian?
│   α = 0.8026570431688571 - 1.091324247760525e-6im
│   β₁ = 1.0720399440829314
│   β₂ = 1.1019028812317075
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -1.1757481594952546e-6 from total weight 1.7331994241999757: operator might not be hermitian?
│   α = 0.866234625976551 - 1.1757481594952546e-6im
│   β₁ = 1.1019028812317075
│   β₂ = 1.0195233480103687
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS  29:	obj = -1.409357861027e-01	err = 3.5767477119e-01	time = 0.03 sec
[ Info: VUMPS  30:	obj = -2.045532833861e-01	err = 3.6013137514e-01	time = 0.02 sec
[ Info: VUMPS  31:	obj = -3.677340068350e-01	err = 2.9848315584e-01	time = 0.02 sec
[ Info: VUMPS  32:	obj = -3.332844888666e-01	err = 3.3334001697e-01	time = 0.06 sec
[ Info: VUMPS  33:	obj = -2.919507908127e-01	err = 3.5475313994e-01	time = 0.03 sec
[ Info: VUMPS  34:	obj = -2.808449276253e-02	err = 3.6950599342e-01	time = 0.08 sec
[ Info: VUMPS  35:	obj = -9.830142151296e-02	err = 3.7023131749e-01	time = 0.06 sec
[ Info: VUMPS  36:	obj = -2.504433745603e-01	err = 3.5111294760e-01	time = 0.02 sec
[ Info: VUMPS  37:	obj = -3.194192131126e-01	err = 3.2385721415e-01	time = 0.02 sec
[ Info: VUMPS  38:	obj = +8.884748290821e-02	err = 3.9871163038e-01	time = 0.07 sec
[ Info: VUMPS  39:	obj = -1.989518543281e-01	err = 3.6796439117e-01	time = 0.02 sec
[ Info: VUMPS  40:	obj = -2.568596388181e-01	err = 3.5396377788e-01	time = 0.02 sec
[ Info: VUMPS  41:	obj = -1.742517027774e-01	err = 3.7560253512e-01	time = 0.03 sec
[ Info: VUMPS  42:	obj = -2.181842216501e-01	err = 3.7550074763e-01	time = 0.02 sec
[ Info: VUMPS  43:	obj = -6.227109008840e-02	err = 4.1909295201e-01	time = 0.05 sec
[ Info: VUMPS  44:	obj = -7.668274105361e-02	err = 4.0844645003e-01	time = 0.03 sec
[ Info: VUMPS  45:	obj = -1.835375816162e-01	err = 3.4820396366e-01	time = 0.02 sec
[ Info: VUMPS  46:	obj = -6.357716783443e-02	err = 3.7708810363e-01	time = 0.02 sec
[ Info: VUMPS  47:	obj = +1.388559492933e-04 -5.781399664562e-15im	err = 3.6961508021e-01	time = 0.05 sec
[ Info: VUMPS  48:	obj = -1.404104902042e-01	err = 3.9016059615e-01	time = 0.02 sec
[ Info: VUMPS  49:	obj = -2.106708660955e-01	err = 3.6760368335e-01	time = 0.02 sec
[ Info: VUMPS  50:	obj = +1.735796736157e-01	err = 3.5521706372e-01	time = 0.02 sec
[ Info: VUMPS  51:	obj = -5.367170688984e-02	err = 3.9109124649e-01	time = 0.06 sec
[ Info: VUMPS  52:	obj = -2.298653965104e-01	err = 3.3926679477e-01	time = 0.02 sec
[ Info: VUMPS  53:	obj = -3.165325039869e-01	err = 3.3133971575e-01	time = 0.02 sec
[ Info: VUMPS  54:	obj = -2.950197697207e-01	err = 3.4876181076e-01	time = 0.03 sec
[ Info: VUMPS  55:	obj = -2.374027247452e-01	err = 3.7519899465e-01	time = 0.06 sec
[ Info: VUMPS  56:	obj = -1.619819474039e-02	err = 3.7718729795e-01	time = 0.02 sec
[ Info: VUMPS  57:	obj = -1.705343092043e-01	err = 3.8558807493e-01	time = 0.02 sec
[ Info: VUMPS  58:	obj = -3.730847939935e-01	err = 2.8129746259e-01	time = 0.02 sec
[ Info: VUMPS  59:	obj = -2.151394001240e-01	err = 4.1030105789e-01	time = 0.06 sec
[ Info: VUMPS  60:	obj = -1.561041094602e-01	err = 3.9671982762e-01	time = 0.02 sec
[ Info: VUMPS  61:	obj = -9.599837934985e-02	err = 3.8528434214e-01	time = 0.02 sec
[ Info: VUMPS  62:	obj = -2.825562036813e-01	err = 3.3900898933e-01	time = 0.02 sec
[ Info: VUMPS  63:	obj = -1.332286499835e-02	err = 3.8572490466e-01	time = 0.06 sec
[ Info: VUMPS  64:	obj = -1.912868202818e-02	err = 3.9649310912e-01	time = 0.02 sec
[ Info: VUMPS  65:	obj = -3.005244814032e-02	err = 4.1809852519e-01	time = 0.02 sec
[ Info: VUMPS  66:	obj = -1.895637479899e-01	err = 3.5881009323e-01	time = 0.05 sec
[ Info: VUMPS  67:	obj = -2.664858728631e-01	err = 3.6123422433e-01	time = 0.03 sec
[ Info: VUMPS  68:	obj = -2.080458300379e-01	err = 3.8597810940e-01	time = 0.03 sec
[ Info: VUMPS  69:	obj = -3.878141128139e-01	err = 2.6683063405e-01	time = 0.02 sec
[ Info: VUMPS  70:	obj = -4.330198106833e-01	err = 1.1995217484e-01	time = 0.08 sec
[ Info: VUMPS  71:	obj = -7.298278720525e-02	err = 3.8622717637e-01	time = 0.03 sec
[ Info: VUMPS  72:	obj = -2.945720162791e-01	err = 3.5422369206e-01	time = 0.02 sec
[ Info: VUMPS  73:	obj = -3.416537322445e-01	err = 3.1228535420e-01	time = 0.02 sec
[ Info: VUMPS  74:	obj = -3.331595948832e-01	err = 3.4179032729e-01	time = 0.06 sec
[ Info: VUMPS  75:	obj = -1.222292014205e-01	err = 4.0978910412e-01	time = 0.03 sec
[ Info: VUMPS  76:	obj = -6.382262951270e-02	err = 3.8950144913e-01	time = 0.04 sec
[ Info: VUMPS  77:	obj = -2.249182124905e-01	err = 3.6705315029e-01	time = 0.06 sec
[ Info: VUMPS  78:	obj = -3.169211687090e-01	err = 3.1190417293e-01	time = 0.03 sec
[ Info: VUMPS  79:	obj = -3.795013187369e-01	err = 2.8575855105e-01	time = 0.04 sec
[ Info: VUMPS  80:	obj = -3.541737574468e-01	err = 3.1274076174e-01	time = 0.03 sec
[ Info: VUMPS  81:	obj = -1.482341913801e-01	err = 3.9486023268e-01	time = 0.06 sec
[ Info: VUMPS  82:	obj = -2.431823642066e-01	err = 3.5485354611e-01	time = 0.03 sec
[ Info: VUMPS  83:	obj = -1.426154410251e-01	err = 3.9431885582e-01	time = 0.02 sec
[ Info: VUMPS  84:	obj = -1.879354265828e-01	err = 3.7761650164e-01	time = 0.06 sec
[ Info: VUMPS  85:	obj = -3.883275844777e-02	err = 3.3484189710e-01	time = 0.03 sec
[ Info: VUMPS  86:	obj = -2.541785323711e-01	err = 3.6013211771e-01	time = 0.02 sec
[ Info: VUMPS  87:	obj = -3.516595702805e-01	err = 3.0264434875e-01	time = 0.03 sec
[ Info: VUMPS  88:	obj = -2.234563948608e-01	err = 3.6699482034e-01	time = 0.05 sec
[ Info: VUMPS  89:	obj = +2.492258044917e-02	err = 3.8778077237e-01	time = 0.02 sec
[ Info: VUMPS  90:	obj = -3.286041797336e-01	err = 3.2736069863e-01	time = 0.02 sec
[ Info: VUMPS  91:	obj = -2.158862857429e-01	err = 3.7995863438e-01	time = 0.03 sec
[ Info: VUMPS  92:	obj = -2.675801195049e-01	err = 3.6561496937e-01	time = 0.06 sec
[ Info: VUMPS  93:	obj = +5.624309743865e-03	err = 4.2867100082e-01	time = 0.03 sec
[ Info: VUMPS  94:	obj = -1.759420429917e-01	err = 3.9349409438e-01	time = 0.02 sec
[ Info: VUMPS  95:	obj = -3.361200941070e-01	err = 2.9968812876e-01	time = 0.02 sec
[ Info: VUMPS  96:	obj = -2.210577853944e-03	err = 3.9551380217e-01	time = 0.06 sec
[ Info: VUMPS  97:	obj = -2.235056018794e-02	err = 3.9877664313e-01	time = 0.02 sec
[ Info: VUMPS  98:	obj = +1.266964324347e-01	err = 3.5087282451e-01	time = 0.02 sec
[ Info: VUMPS  99:	obj = -1.649834446522e-01	err = 3.7313907507e-01	time = 0.02 sec
[ Info: VUMPS 100:	obj = -2.810724087197e-01	err = 3.4803141841e-01	time = 0.06 sec
[ Info: VUMPS 101:	obj = -3.934095054094e-01	err = 2.5788371653e-01	time = 0.03 sec
[ Info: VUMPS 102:	obj = -2.769141978863e-02	err = 4.2113724750e-01	time = 0.03 sec
[ Info: VUMPS 103:	obj = -1.428941704956e-01	err = 3.7175159384e-01	time = 0.05 sec
[ Info: VUMPS 104:	obj = -2.825079318885e-01	err = 3.4365263618e-01	time = 0.02 sec
[ Info: VUMPS 105:	obj = -3.895828699840e-01	err = 2.5772008058e-01	time = 0.03 sec
[ Info: VUMPS 106:	obj = -3.789769542971e-01	err = 2.7647068815e-01	time = 0.03 sec
[ Info: VUMPS 107:	obj = -4.131370544119e-01	err = 2.0771775492e-01	time = 0.06 sec
[ Info: VUMPS 108:	obj = +1.891808047741e-02	err = 4.0211631708e-01	time = 0.03 sec
[ Info: VUMPS 109:	obj = -3.126203477249e-01	err = 3.3581501662e-01	time = 0.03 sec
[ Info: VUMPS 110:	obj = -3.891256643994e-01	err = 2.6587912557e-01	time = 0.07 sec
[ Info: VUMPS 111:	obj = -3.350222584524e-01	err = 3.2878659423e-01	time = 0.03 sec
[ Info: VUMPS 112:	obj = -3.383500923964e-01	err = 3.0810425001e-01	time = 0.03 sec
[ Info: VUMPS 113:	obj = -2.921012433328e-01	err = 3.5940858624e-01	time = 0.03 sec
[ Info: VUMPS 114:	obj = -3.304195736343e-01	err = 3.2278577971e-01	time = 0.06 sec
[ Info: VUMPS 115:	obj = -1.435645156425e-01	err = 4.0512614823e-01	time = 0.03 sec
[ Info: VUMPS 116:	obj = -1.679237781365e-01	err = 3.6250880408e-01	time = 0.02 sec
[ Info: VUMPS 117:	obj = -1.408768635481e-01	err = 3.6326347756e-01	time = 0.05 sec
[ Info: VUMPS 118:	obj = -1.939462004720e-02	err = 4.0498337302e-01	time = 0.03 sec
[ Info: VUMPS 119:	obj = -2.352201460179e-01	err = 3.6574114214e-01	time = 0.02 sec
[ Info: VUMPS 120:	obj = -2.295422994168e-02	err = 3.6188803296e-01	time = 0.03 sec
[ Info: VUMPS 121:	obj = -6.989486583808e-02	err = 3.7006193288e-01	time = 0.05 sec
[ Info: VUMPS 122:	obj = -3.493531583983e-02	err = 3.8804888357e-01	time = 0.03 sec
[ Info: VUMPS 123:	obj = +7.790731640126e-04	err = 3.8138863176e-01	time = 0.02 sec
[ Info: VUMPS 124:	obj = -1.919530149789e-01	err = 3.6070095280e-01	time = 0.03 sec
[ Info: VUMPS 125:	obj = -3.218424809114e-01	err = 3.3338267984e-01	time = 0.05 sec
[ Info: VUMPS 126:	obj = -3.667333159463e-01	err = 2.8821000587e-01	time = 0.02 sec
[ Info: VUMPS 127:	obj = -2.130648461950e-01	err = 3.7595362973e-01	time = 0.03 sec
[ Info: VUMPS 128:	obj = -1.030371749297e-01	err = 4.2417993413e-01	time = 0.03 sec
[ Info: VUMPS 129:	obj = -1.830830998421e-01	err = 3.7685385391e-01	time = 0.05 sec
[ Info: VUMPS 130:	obj = -7.071567794803e-02	err = 3.9744980880e-01	time = 0.02 sec
[ Info: VUMPS 131:	obj = -4.769518696950e-02	err = 3.8112218583e-01	time = 0.02 sec
[ Info: VUMPS 132:	obj = -2.991402416948e-01	err = 3.3370573847e-01	time = 0.02 sec
[ Info: VUMPS 133:	obj = -2.746313335444e-01	err = 3.5097484163e-01	time = 0.06 sec
[ Info: VUMPS 134:	obj = -3.276842746897e-01	err = 3.1708681372e-01	time = 0.02 sec
[ Info: VUMPS 135:	obj = -2.049761563157e-01	err = 3.7370273426e-01	time = 0.02 sec
[ Info: VUMPS 136:	obj = -3.833983237486e-01	err = 2.6114682914e-01	time = 0.02 sec
[ Info: VUMPS 137:	obj = -6.177005685578e-02	err = 3.8019469489e-01	time = 0.06 sec
[ Info: VUMPS 138:	obj = -1.316570790104e-01	err = 3.8729233886e-01	time = 0.02 sec
[ Info: VUMPS 139:	obj = -2.366225337929e-01	err = 3.6759309875e-01	time = 0.03 sec
[ Info: VUMPS 140:	obj = +8.913339361766e-02	err = 3.7167547836e-01	time = 0.08 sec
[ Info: VUMPS 141:	obj = -7.481699300835e-02	err = 3.8011320937e-01	time = 0.04 sec
[ Info: VUMPS 142:	obj = -2.554895657661e-01	err = 3.5626764832e-01	time = 0.03 sec
[ Info: VUMPS 143:	obj = -2.752729453871e-01	err = 3.5827930411e-01	time = 0.03 sec
[ Info: VUMPS 144:	obj = -1.078710456452e-01	err = 3.7452629595e-01	time = 0.06 sec
[ Info: VUMPS 145:	obj = -1.834468230261e-01	err = 3.9202973168e-01	time = 0.03 sec
[ Info: VUMPS 146:	obj = -2.880934140139e-01	err = 3.4460619232e-01	time = 0.04 sec
[ Info: VUMPS 147:	obj = -2.585829024830e-01	err = 3.4906000653e-01	time = 0.03 sec
[ Info: VUMPS 148:	obj = -7.446540858731e-02	err = 4.2725017960e-01	time = 0.06 sec
[ Info: VUMPS 149:	obj = +1.223133246756e-02	err = 4.2025804351e-01	time = 0.02 sec
[ Info: VUMPS 150:	obj = -7.807677131111e-02	err = 4.0384260646e-01	time = 0.02 sec
[ Info: VUMPS 151:	obj = -1.510082807256e-01	err = 4.1367387477e-01	time = 0.03 sec
[ Info: VUMPS 152:	obj = -1.077844357575e-01	err = 3.8783544296e-01	time = 0.05 sec
[ Info: VUMPS 153:	obj = -2.687661583404e-01	err = 3.5954953023e-01	time = 0.02 sec
[ Info: VUMPS 154:	obj = -2.216118903419e-01	err = 3.6631386313e-01	time = 0.03 sec
[ Info: VUMPS 155:	obj = -3.346454865703e-03	err = 3.7228195751e-01	time = 0.03 sec
[ Info: VUMPS 156:	obj = -2.182777019563e-01	err = 3.7120325813e-01	time = 0.06 sec
[ Info: VUMPS 157:	obj = -2.260481514080e-01	err = 3.7084200121e-01	time = 0.03 sec
[ Info: VUMPS 158:	obj = -3.753639631248e-01	err = 2.8129702848e-01	time = 0.02 sec
[ Info: VUMPS 159:	obj = +1.493818093509e-01	err = 3.5990583300e-01	time = 0.06 sec
[ Info: VUMPS 160:	obj = -7.335279560891e-02	err = 3.8634405938e-01	time = 0.02 sec
[ Info: VUMPS 161:	obj = -1.712788073268e-01	err = 3.8098418215e-01	time = 0.03 sec
[ Info: VUMPS 162:	obj = -2.775045952826e-02	err = 3.6432182146e-01	time = 0.03 sec
[ Info: VUMPS 163:	obj = -2.974540518908e-01	err = 3.2120804570e-01	time = 0.06 sec
[ Info: VUMPS 164:	obj = -4.054076797989e-01	err = 2.3514693235e-01	time = 0.04 sec
[ Info: VUMPS 165:	obj = -7.519182934781e-02	err = 4.0110456979e-01	time = 0.03 sec
[ Info: VUMPS 166:	obj = -1.784723524117e-01	err = 3.8591296831e-01	time = 0.02 sec
[ Info: VUMPS 167:	obj = -1.116507302906e-01	err = 3.7195004686e-01	time = 0.06 sec
[ Info: VUMPS 168:	obj = -3.122365679686e-01	err = 3.3350953764e-01	time = 0.02 sec
[ Info: VUMPS 169:	obj = -3.560972462991e-01	err = 2.8786350505e-01	time = 0.03 sec
[ Info: VUMPS 170:	obj = -2.497036138206e-01	err = 3.7652961352e-01	time = 0.03 sec
[ Info: VUMPS 171:	obj = -1.204935017155e-01	err = 3.7477170313e-01	time = 0.06 sec
[ Info: VUMPS 172:	obj = -3.140736291711e-01	err = 3.3651541095e-01	time = 0.02 sec
[ Info: VUMPS 173:	obj = -3.777537348031e-01	err = 2.8281048666e-01	time = 0.03 sec
[ Info: VUMPS 174:	obj = -4.081318507282e-01	err = 2.2729687790e-01	time = 0.06 sec
[ Info: VUMPS 175:	obj = +8.272685287566e-03	err = 4.2559224619e-01	time = 0.03 sec
[ Info: VUMPS 176:	obj = -1.393268322253e-01	err = 3.9579900440e-01	time = 0.03 sec
[ Info: VUMPS 177:	obj = -9.734245038937e-02	err = 3.5396586975e-01	time = 0.03 sec
[ Info: VUMPS 178:	obj = -2.821477914715e-01	err = 3.5794786333e-01	time = 0.06 sec
[ Info: VUMPS 179:	obj = -4.040896409723e-01	err = 2.2336565394e-01	time = 0.03 sec
[ Info: VUMPS 180:	obj = +8.386756242174e-03	err = 4.0133165398e-01	time = 0.02 sec
[ Info: VUMPS 181:	obj = -1.390628324690e-01	err = 3.5859390916e-01	time = 0.05 sec
[ Info: VUMPS 182:	obj = -1.281482713515e-01	err = 3.6674107529e-01	time = 0.02 sec
[ Info: VUMPS 183:	obj = -9.466660283788e-02	err = 4.0504716786e-01	time = 0.03 sec
[ Info: VUMPS 184:	obj = -1.755981307732e-01	err = 3.8378790855e-01	time = 0.02 sec
[ Info: VUMPS 185:	obj = -9.036868885930e-02	err = 3.6141032024e-01	time = 0.05 sec
[ Info: VUMPS 186:	obj = -3.703625904624e-01	err = 2.8654729147e-01	time = 0.02 sec
[ Info: VUMPS 187:	obj = -3.162732937988e-01	err = 3.4485685016e-01	time = 0.03 sec
[ Info: VUMPS 188:	obj = -1.112394896513e-01	err = 3.9807795128e-01	time = 0.03 sec
[ Info: VUMPS 189:	obj = +1.824853010192e-03	err = 3.9447516200e-01	time = 0.06 sec
[ Info: VUMPS 190:	obj = -2.140867094456e-01	err = 3.7898558231e-01	time = 0.02 sec
[ Info: VUMPS 191:	obj = +4.894440406361e-02	err = 3.9055437558e-01	time = 0.02 sec
[ Info: VUMPS 192:	obj = -3.751396808486e-02	err = 3.8799740635e-01	time = 0.02 sec
[ Info: VUMPS 193:	obj = -1.682962360358e-01	err = 3.7336809188e-01	time = 0.05 sec
[ Info: VUMPS 194:	obj = -1.748904771170e-01	err = 3.3383969111e-01	time = 0.02 sec
[ Info: VUMPS 195:	obj = -2.023258032592e-01	err = 3.5779592817e-01	time = 0.02 sec
[ Info: VUMPS 196:	obj = -2.562842975568e-01	err = 3.5451811621e-01	time = 0.03 sec
[ Info: VUMPS 197:	obj = -1.198772391755e-01	err = 3.8884771754e-01	time = 0.06 sec
[ Info: VUMPS 198:	obj = -1.194696203501e-01	err = 3.6306124333e-01	time = 0.03 sec
[ Info: VUMPS 199:	obj = -3.165670058206e-01	err = 3.4580209634e-01	time = 0.03 sec
┌ Warning: VUMPS cancel 200:	obj = -3.605645351808e-01	err = 3.2889262642e-01	time = 6.93 sec
└ @ MPSKit ~/Projects/MPSKit.jl/src/algorithms/groundstate/vumps.jl:67

As you can see, VUMPS struggles to converge. On it's own, that is already quite curious. Maybe we can do better using another algorithm, such as gradient descent.

groundstate, cache, delta = find_groundstate(state, H, GradientGrassmann(; maxiter=20));

[ Info: CG: initializing with f = 0.249997124956, ‖∇f‖ = 3.4016e-03
[ Info: CG: iter    1: f = -0.025384109228, ‖∇f‖ = 6.9269e-01, α = 8.72e+05, β = 0.00e+00, nfg = 18
[ Info: CG: iter    2: f = -0.034734780784, ‖∇f‖ = 6.7957e-01, α = 3.41e-02, β = 2.69e+04, nfg = 19
[ Info: CG: iter    3: f = -0.035137291778, ‖∇f‖ = 6.6715e-01, α = 5.70e-03, β = 4.46e-01, nfg = 3
┌ Warning: resorting to η
└ @ OptimKit ~/.julia/packages/OptimKit/xpmbV/src/cg.jl:139
[ Info: CG: iter    4: f = -0.230959138308, ‖∇f‖ = 6.9544e-01, α = 1.02e+00, β = -2.32e-04, nfg = 5
[ Info: CG: iter    5: f = -0.344516007182, ‖∇f‖ = 5.3414e-01, α = 7.93e-01, β = 3.06e-01, nfg = 3
[ Info: CG: iter    6: f = -0.394577435495, ‖∇f‖ = 4.0969e-01, α = 7.63e-01, β = 1.75e-01, nfg = 2
[ Info: CG: iter    7: f = -0.423605152054, ‖∇f‖ = 2.3260e-01, α = 5.92e-01, β = 1.59e-01, nfg = 2
[ Info: CG: iter    8: f = -0.433877622086, ‖∇f‖ = 1.0355e-01, α = 4.39e-01, β = 1.19e-01, nfg = 2
[ Info: CG: iter    9: f = -0.436274421836, ‖∇f‖ = 7.4845e-02, α = 3.14e-01, β = 2.45e-01, nfg = 2
[ Info: CG: iter   10: f = -0.437275612812, ‖∇f‖ = 6.7115e-02, α = 1.56e-01, β = 6.92e-01, nfg = 2
[ Info: CG: iter   11: f = -0.438430268284, ‖∇f‖ = 6.7977e-02, α = 3.09e-01, β = 4.96e-01, nfg = 2
[ Info: CG: iter   12: f = -0.439719125881, ‖∇f‖ = 5.3438e-02, α = 4.32e-01, β = 3.51e-01, nfg = 2
[ Info: CG: iter   13: f = -0.440296278919, ‖∇f‖ = 4.4785e-02, α = 2.16e-01, β = 5.24e-01, nfg = 2
[ Info: CG: iter   14: f = -0.440794890531, ‖∇f‖ = 3.8641e-02, α = 2.22e-01, β = 6.23e-01, nfg = 2
[ Info: CG: iter   15: f = -0.441206155655, ‖∇f‖ = 3.7357e-02, α = 3.41e-01, β = 3.86e-01, nfg = 2
[ Info: CG: iter   16: f = -0.441529728743, ‖∇f‖ = 3.0799e-02, α = 2.78e-01, β = 4.26e-01, nfg = 2
[ Info: CG: iter   17: f = -0.441770475509, ‖∇f‖ = 2.7481e-02, α = 2.52e-01, β = 5.75e-01, nfg = 2
[ Info: CG: iter   18: f = -0.441987084171, ‖∇f‖ = 2.5934e-02, α = 3.26e-01, β = 4.60e-01, nfg = 2
[ Info: CG: iter   19: f = -0.442146991122, ‖∇f‖ = 2.3586e-02, α = 2.69e-01, β = 5.43e-01, nfg = 2
┌ Warning: CG: not converged to requested tol: f = -0.442291713427, ‖∇f‖ = 2.0461e-02
└ @ OptimKit ~/.julia/packages/OptimKit/xpmbV/src/cg.jl:103

Convergence is quite slow and even fails after sufficiently many iterations. To understand why, we can look at the transfer matrix spectrum.

transferplot(groundstate, groundstate)

We can clearly see multiple eigenvalues close to the unit circle. Our state is close to being non-injective, and represents the sum of multiple injective states. This is numerically very problematic, but also indicates that we used an incorrect ansatz to approximate the groundstate. We should retry with a larger unit cell.

Success

Let's initialize a different initial state, this time with a 2-site unit cell:

A = TensorMap(rand, ComplexF64, ℂ^20 * ℂ^2, ℂ^20);
B = TensorMap(rand, ComplexF64, ℂ^20 * ℂ^2, ℂ^20);
state = InfiniteMPS([A, B]);

In MPSKit, we require that the periodicity of the hamiltonian equals that of the state it is applied to. This is not a big obstacle, you can simply repeat the original hamiltonian. Alternatively, the hamiltonian can be constructed directly on a two-site unitcell by making use of MPSKitModels.jl's @mpoham.

# H2 = repeat(H, 2); -- copies the one-site version
H2 = heisenberg_XXX(ComplexF64, Trivial, InfiniteChain(2); spin=1 // 2)
groundstate, cache, delta = find_groundstate(state, H2,
                                             VUMPS(; maxiter=100, tol=1e-12));

[ Info: VUMPS init:	obj = +4.994034626541e-01	err = 5.1147e-02
[ Info: VUMPS   1:	obj = -6.262869203043e-02	err = 3.8580046779e-01	time = 0.11 sec
[ Info: VUMPS   2:	obj = -8.607141221574e-01	err = 1.2356188469e-01	time = 0.02 sec
[ Info: VUMPS   3:	obj = -8.851326788898e-01	err = 1.3843868842e-02	time = 0.02 sec
[ Info: VUMPS   4:	obj = -8.859081586783e-01	err = 6.1401047820e-03	time = 0.03 sec
[ Info: VUMPS   5:	obj = -8.861065721524e-01	err = 4.0177146467e-03	time = 0.03 sec
[ Info: VUMPS   6:	obj = -8.861785252458e-01	err = 2.7819071955e-03	time = 0.05 sec
[ Info: VUMPS   7:	obj = -8.862090474504e-01	err = 2.0054538265e-03	time = 0.09 sec
[ Info: VUMPS   8:	obj = -8.862231227796e-01	err = 1.4866506538e-03	time = 0.03 sec
[ Info: VUMPS   9:	obj = -8.862299174133e-01	err = 1.0781153418e-03	time = 0.03 sec
[ Info: VUMPS  10:	obj = -8.862332526284e-01	err = 8.0176561905e-04	time = 0.04 sec
[ Info: VUMPS  11:	obj = -8.862349227193e-01	err = 5.9244791851e-04	time = 0.07 sec
[ Info: VUMPS  12:	obj = -8.862357635094e-01	err = 4.4166081769e-04	time = 0.04 sec
[ Info: VUMPS  13:	obj = -8.862361924426e-01	err = 3.4628140735e-04	time = 0.04 sec
[ Info: VUMPS  14:	obj = -8.862364148218e-01	err = 2.7392973609e-04	time = 0.07 sec
[ Info: VUMPS  15:	obj = -8.862365333782e-01	err = 2.3548153669e-04	time = 0.04 sec
[ Info: VUMPS  16:	obj = -8.862366003882e-01	err = 2.0924520967e-04	time = 0.07 sec
[ Info: VUMPS  17:	obj = -8.862366415980e-01	err = 1.9635595936e-04	time = 0.04 sec
[ Info: VUMPS  18:	obj = -8.862366705874e-01	err = 1.9049012489e-04	time = 0.07 sec
[ Info: VUMPS  19:	obj = -8.862366940299e-01	err = 1.8899241029e-04	time = 0.04 sec
[ Info: VUMPS  20:	obj = -8.862367155996e-01	err = 1.9097122153e-04	time = 0.07 sec
[ Info: VUMPS  21:	obj = -8.862367373638e-01	err = 1.9481944475e-04	time = 0.05 sec
[ Info: VUMPS  22:	obj = -8.862367604209e-01	err = 2.0067663970e-04	time = 0.09 sec
[ Info: VUMPS  23:	obj = -8.862367858969e-01	err = 2.0818860599e-04	time = 0.04 sec
[ Info: VUMPS  24:	obj = -8.862368141807e-01	err = 2.1736488170e-04	time = 0.07 sec
[ Info: VUMPS  25:	obj = -8.862368464497e-01	err = 2.2859478788e-04	time = 0.04 sec
[ Info: VUMPS  26:	obj = -8.862368828456e-01	err = 2.4175658730e-04	time = 0.07 sec
[ Info: VUMPS  27:	obj = -8.862369249947e-01	err = 2.5762627945e-04	time = 0.04 sec
[ Info: VUMPS  28:	obj = -8.862369728770e-01	err = 2.7619128372e-04	time = 0.07 sec
[ Info: VUMPS  29:	obj = -8.862370289739e-01	err = 2.9841300959e-04	time = 0.05 sec
[ Info: VUMPS  30:	obj = -8.862370930650e-01	err = 3.2477737551e-04	time = 0.07 sec
[ Info: VUMPS  31:	obj = -8.862371692951e-01	err = 3.5590713379e-04	time = 0.04 sec
[ Info: VUMPS  32:	obj = -8.862372570904e-01	err = 3.9353059847e-04	time = 0.07 sec
[ Info: VUMPS  33:	obj = -8.862373640071e-01	err = 4.3603005725e-04	time = 0.04 sec
[ Info: VUMPS  34:	obj = -8.862374883321e-01	err = 4.8815487884e-04	time = 0.07 sec
[ Info: VUMPS  35:	obj = -8.862376445282e-01	err = 5.3937202139e-04	time = 0.04 sec
[ Info: VUMPS  36:	obj = -8.862378254047e-01	err = 6.0151343771e-04	time = 0.04 sec
[ Info: VUMPS  37:	obj = -8.862380560924e-01	err = 6.3791369135e-04	time = 0.07 sec
[ Info: VUMPS  38:	obj = -8.862383068811e-01	err = 6.7996919433e-04	time = 0.04 sec
[ Info: VUMPS  39:	obj = -8.862386058811e-01	err = 6.4634261288e-04	time = 0.08 sec
[ Info: VUMPS  40:	obj = -8.862388802875e-01	err = 6.2080152793e-04	time = 0.04 sec
[ Info: VUMPS  41:	obj = -8.862391460561e-01	err = 5.0675637451e-04	time = 0.08 sec
[ Info: VUMPS  42:	obj = -8.862393416168e-01	err = 4.2985263716e-04	time = 0.04 sec
[ Info: VUMPS  43:	obj = -8.862394885298e-01	err = 3.1911525906e-04	time = 0.08 sec
[ Info: VUMPS  44:	obj = -8.862395827629e-01	err = 2.5276803245e-04	time = 0.04 sec
[ Info: VUMPS  45:	obj = -8.862396443908e-01	err = 1.8512521569e-04	time = 0.08 sec
[ Info: VUMPS  46:	obj = -8.862396829362e-01	err = 1.4700821652e-04	time = 0.04 sec
[ Info: VUMPS  47:	obj = -8.862397077973e-01	err = 1.1022783530e-04	time = 0.07 sec
[ Info: VUMPS  48:	obj = -8.862397240917e-01	err = 9.2219279764e-05	time = 0.04 sec
[ Info: VUMPS  49:	obj = -8.862397352818e-01	err = 7.1892346813e-05	time = 0.07 sec
[ Info: VUMPS  50:	obj = -8.862397433166e-01	err = 6.5073723507e-05	time = 0.04 sec
[ Info: VUMPS  51:	obj = -8.862397493970e-01	err = 5.5282518065e-05	time = 0.08 sec
[ Info: VUMPS  52:	obj = -8.862397542161e-01	err = 5.1456531474e-05	time = 0.04 sec
[ Info: VUMPS  53:	obj = -8.862397581953e-01	err = 4.6714202684e-05	time = 0.08 sec
[ Info: VUMPS  54:	obj = -8.862397615871e-01	err = 4.3942466103e-05	time = 0.04 sec
[ Info: VUMPS  55:	obj = -8.862397645493e-01	err = 4.1177713870e-05	time = 0.07 sec
[ Info: VUMPS  56:	obj = -8.862397671820e-01	err = 3.9114982243e-05	time = 0.04 sec
[ Info: VUMPS  57:	obj = -8.862397695517e-01	err = 3.7186097920e-05	time = 0.07 sec
[ Info: VUMPS  58:	obj = -8.862397717040e-01	err = 3.5553409941e-05	time = 0.04 sec
[ Info: VUMPS  59:	obj = -8.862397736718e-01	err = 3.4038601553e-05	time = 0.08 sec
[ Info: VUMPS  60:	obj = -8.862397754798e-01	err = 3.2679861075e-05	time = 0.04 sec
[ Info: VUMPS  61:	obj = -8.862397771471e-01	err = 3.1412139117e-05	time = 0.07 sec
[ Info: VUMPS  62:	obj = -8.862397786894e-01	err = 3.0244528404e-05	time = 0.04 sec
[ Info: VUMPS  63:	obj = -8.862397801195e-01	err = 2.9148581648e-05	time = 0.07 sec
[ Info: VUMPS  64:	obj = -8.862397814483e-01	err = 2.8125831750e-05	time = 0.04 sec
[ Info: VUMPS  65:	obj = -8.862397826855e-01	err = 2.7161607890e-05	time = 0.07 sec
[ Info: VUMPS  66:	obj = -8.862397838391e-01	err = 2.6254981486e-05	time = 0.04 sec
[ Info: VUMPS  67:	obj = -8.862397849165e-01	err = 2.5397377333e-05	time = 0.07 sec
[ Info: VUMPS  68:	obj = -8.862397859242e-01	err = 2.4587152172e-05	time = 0.04 sec
[ Info: VUMPS  69:	obj = -8.862397868680e-01	err = 2.3818718802e-05	time = 0.07 sec
[ Info: VUMPS  70:	obj = -8.862397877531e-01	err = 2.3090202212e-05	time = 0.04 sec
[ Info: VUMPS  71:	obj = -8.862397885843e-01	err = 2.2397708419e-05	time = 0.07 sec
[ Info: VUMPS  72:	obj = -8.862397893656e-01	err = 2.1739356071e-05	time = 0.04 sec
[ Info: VUMPS  73:	obj = -8.862397901011e-01	err = 2.1112310644e-05	time = 0.07 sec
[ Info: VUMPS  74:	obj = -8.862397907941e-01	err = 2.0514795921e-05	time = 0.04 sec
[ Info: VUMPS  75:	obj = -8.862397914478e-01	err = 1.9944644746e-05	time = 0.07 sec
[ Info: VUMPS  76:	obj = -8.862397920651e-01	err = 1.9400238943e-05	time = 0.04 sec
[ Info: VUMPS  77:	obj = -8.862397926487e-01	err = 1.8879869617e-05	time = 0.07 sec
[ Info: VUMPS  78:	obj = -8.862397932009e-01	err = 1.8382107216e-05	time = 0.04 sec
[ Info: VUMPS  79:	obj = -8.862397937239e-01	err = 1.7905544693e-05	time = 0.07 sec
[ Info: VUMPS  80:	obj = -8.862397942198e-01	err = 1.7448935744e-05	time = 0.04 sec
[ Info: VUMPS  81:	obj = -8.862397946902e-01	err = 1.7011113669e-05	time = 0.07 sec
[ Info: VUMPS  82:	obj = -8.862397951371e-01	err = 1.6590972981e-05	time = 0.04 sec
[ Info: VUMPS  83:	obj = -8.862397955618e-01	err = 1.6187537766e-05	time = 0.07 sec
[ Info: VUMPS  84:	obj = -8.862397959658e-01	err = 1.5799851792e-05	time = 0.04 sec
[ Info: VUMPS  85:	obj = -8.862397963505e-01	err = 1.5427072391e-05	time = 0.07 sec
[ Info: VUMPS  86:	obj = -8.862397967170e-01	err = 1.5068369727e-05	time = 0.06 sec
[ Info: VUMPS  87:	obj = -8.862397970664e-01	err = 1.4723011390e-05	time = 0.09 sec
[ Info: VUMPS  88:	obj = -8.862397973998e-01	err = 1.4390277758e-05	time = 0.04 sec
[ Info: VUMPS  89:	obj = -8.862397977181e-01	err = 1.4069534998e-05	time = 0.07 sec
[ Info: VUMPS  90:	obj = -8.862397980223e-01	err = 1.3760148626e-05	time = 0.04 sec
[ Info: VUMPS  91:	obj = -8.862397983131e-01	err = 1.3461564491e-05	time = 0.07 sec
[ Info: VUMPS  92:	obj = -8.862397985912e-01	err = 1.3173227645e-05	time = 0.04 sec
[ Info: VUMPS  93:	obj = -8.862397988575e-01	err = 1.2894656269e-05	time = 0.07 sec
[ Info: VUMPS  94:	obj = -8.862397991125e-01	err = 1.2625358983e-05	time = 0.04 sec
[ Info: VUMPS  95:	obj = -8.862397993569e-01	err = 1.2364911249e-05	time = 0.07 sec
[ Info: VUMPS  96:	obj = -8.862397995913e-01	err = 1.2112879975e-05	time = 0.04 sec
[ Info: VUMPS  97:	obj = -8.862397998161e-01	err = 1.1868886466e-05	time = 0.07 sec
[ Info: VUMPS  98:	obj = -8.862398000318e-01	err = 1.1632550359e-05	time = 0.04 sec
[ Info: VUMPS  99:	obj = -8.862398002390e-01	err = 1.1403537234e-05	time = 0.07 sec
┌ Warning: VUMPS cancel 100:	obj = -8.862398004381e-01	err = 1.1181508752e-05	time = 5.61 sec
└ @ MPSKit ~/Projects/MPSKit.jl/src/algorithms/groundstate/vumps.jl:67

We get convergence, but it takes an enormous amount of iterations. The reason behind this becomes more obvious at higher bond dimensions:

groundstate, cache, delta = find_groundstate(state, H2,
                                             IDMRG2(; trscheme=truncdim(50), maxiter=20,
                                                    tol=1e-12))
entanglementplot(groundstate)

We see that some eigenvalues clearly belong to a group, and are almost degenerate. This implies 2 things:

• there is superfluous information, if those eigenvalues are the same anyway
• poor convergence if we cut off within such a subspace

It are precisely those problems that we can solve by using symmetries.

Symmetries

The XXZ Heisenberg hamiltonian is SU(2) symmetric and we can exploit this to greatly speed up the simulation.

It is cumbersome to construct symmetric hamiltonians, but luckily su(2) symmetric XXZ is already implemented:

H2 = heisenberg_XXX(ComplexF64, SU2Irrep, InfiniteChain(2); spin=1 // 2);

Our initial state should also be SU(2) symmetric. It now becomes apparent why we have to use a two-site periodic state. The physical space carries a half-integer charge and the first tensor maps the first virtual_space ⊗ the physical_space to the second virtual_space. Half-integer virtual charges will therefore map only to integer charges, and vice versa. The staggering thus happens on the virtual level.

An alternative constructor for the initial state is

P = Rep[SU₂](1 // 2 => 1)
V1 = Rep[SU₂](1 // 2 => 10, 3 // 2 => 5, 5 // 2 => 2)
V2 = Rep[SU₂](0 => 15, 1 => 10, 2 => 5)
state = InfiniteMPS([P, P], [V1, V2]);

┌ Warning: Constructing an MPS from tensors that are not full rank
└ @ MPSKit ~/Projects/MPSKit.jl/src/states/infinitemps.jl:149

Even though the bond dimension is higher than in the example without symmetry, convergence is reached much faster:

println(dim(V1))
println(dim(V2))
groundstate, cache, delta = find_groundstate(state, H2,
                                             VUMPS(; maxiter=400, tol=1e-12));

52
70
[ Info: VUMPS init:	obj = +4.207308597914e-02	err = 3.8417e-01
[ Info: VUMPS   1:	obj = -8.770246689397e-01	err = 8.9387480236e-02	time = 0.09 sec
[ Info: VUMPS   2:	obj = -8.854224662459e-01	err = 1.2035494481e-02	time = 0.08 sec
[ Info: VUMPS   3:	obj = -8.860742922774e-01	err = 4.4294789545e-03	time = 0.08 sec
[ Info: VUMPS   4:	obj = -8.862108801823e-01	err = 1.9061849051e-03	time = 0.09 sec
[ Info: VUMPS   5:	obj = -8.862567332668e-01	err = 1.1244944387e-03	time = 0.11 sec
[ Info: VUMPS   6:	obj = -8.862739286226e-01	err = 8.4129140580e-04	time = 0.12 sec
[ Info: VUMPS   7:	obj = -8.862812942419e-01	err = 6.3937860306e-04	time = 0.23 sec
[ Info: VUMPS   8:	obj = -8.862846581258e-01	err = 5.2763554024e-04	time = 0.12 sec
[ Info: VUMPS   9:	obj = -8.862862830189e-01	err = 4.2102561366e-04	time = 0.12 sec
[ Info: VUMPS  10:	obj = -8.862870857559e-01	err = 3.3035934875e-04	time = 0.13 sec
[ Info: VUMPS  11:	obj = -8.862874886043e-01	err = 2.5432646892e-04	time = 0.13 sec
[ Info: VUMPS  12:	obj = -8.862876919660e-01	err = 1.9202079806e-04	time = 0.21 sec
[ Info: VUMPS  13:	obj = -8.862877946054e-01	err = 1.4279990039e-04	time = 0.19 sec
[ Info: VUMPS  14:	obj = -8.862878462682e-01	err = 1.0491846055e-04	time = 0.14 sec
[ Info: VUMPS  15:	obj = -8.862878721892e-01	err = 7.6390575113e-05	time = 0.20 sec
[ Info: VUMPS  16:	obj = -8.862878851596e-01	err = 5.5250778998e-05	time = 0.14 sec
[ Info: VUMPS  17:	obj = -8.862878916381e-01	err = 3.9767417638e-05	time = 0.15 sec
[ Info: VUMPS  18:	obj = -8.862878948705e-01	err = 2.8521655196e-05	time = 0.20 sec
[ Info: VUMPS  19:	obj = -8.862878964826e-01	err = 2.0403457752e-05	time = 0.15 sec
[ Info: VUMPS  20:	obj = -8.862878972865e-01	err = 1.4568719674e-05	time = 0.15 sec
[ Info: VUMPS  21:	obj = -8.862878976876e-01	err = 1.0388173825e-05	time = 0.19 sec
[ Info: VUMPS  22:	obj = -8.862878978877e-01	err = 7.3993990730e-06	time = 0.15 sec
[ Info: VUMPS  23:	obj = -8.862878979876e-01	err = 5.2663271673e-06	time = 0.20 sec
[ Info: VUMPS  24:	obj = -8.862878980375e-01	err = 3.7457858907e-06	time = 0.15 sec
[ Info: VUMPS  25:	obj = -8.862878980625e-01	err = 2.6630244108e-06	time = 0.19 sec
[ Info: VUMPS  26:	obj = -8.862878980749e-01	err = 1.8924316652e-06	time = 0.15 sec
[ Info: VUMPS  27:	obj = -8.862878980812e-01	err = 1.3443459346e-06	time = 0.19 sec
[ Info: VUMPS  28:	obj = -8.862878980843e-01	err = 9.5471634701e-07	time = 0.15 sec
[ Info: VUMPS  29:	obj = -8.862878980859e-01	err = 6.7781844497e-07	time = 0.19 sec
[ Info: VUMPS  30:	obj = -8.862878980866e-01	err = 4.8112158398e-07	time = 0.15 sec
[ Info: VUMPS  31:	obj = -8.862878980870e-01	err = 3.4143706519e-07	time = 0.19 sec
[ Info: VUMPS  32:	obj = -8.862878980872e-01	err = 2.4224840418e-07	time = 0.15 sec
[ Info: VUMPS  33:	obj = -8.862878980873e-01	err = 1.7186139672e-07	time = 0.18 sec
[ Info: VUMPS  34:	obj = -8.862878980874e-01	err = 1.2190374782e-07	time = 0.14 sec
[ Info: VUMPS  35:	obj = -8.862878980874e-01	err = 8.6464933933e-08	time = 0.17 sec
[ Info: VUMPS  36:	obj = -8.862878980874e-01	err = 6.1286598356e-08	time = 0.12 sec
[ Info: VUMPS  37:	obj = -8.862878980874e-01	err = 4.3458741190e-08	time = 0.17 sec
[ Info: VUMPS  38:	obj = -8.862878980874e-01	err = 3.0804670453e-08	time = 0.12 sec
[ Info: VUMPS  39:	obj = -8.862878980874e-01	err = 2.1850363058e-08	time = 0.16 sec
[ Info: VUMPS  40:	obj = -8.862878980874e-01	err = 1.5482006174e-08	time = 0.11 sec
[ Info: VUMPS  41:	obj = -8.862878980874e-01	err = 1.0955627446e-08	time = 0.11 sec
[ Info: VUMPS  42:	obj = -8.862878980874e-01	err = 7.7609982125e-09	time = 0.16 sec
[ Info: VUMPS  43:	obj = -8.862878980874e-01	err = 5.4975161355e-09	time = 0.10 sec
[ Info: VUMPS  44:	obj = -8.862878980874e-01	err = 3.8884417026e-09	time = 0.14 sec
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[ Info: VUMPS 228:	obj = -8.862878980874e-01	err = 3.0618708554e-11	time = 0.08 sec
[ Info: VUMPS 229:	obj = -8.862878980874e-01	err = 7.3510645058e-11	time = 0.06 sec
[ Info: VUMPS 230:	obj = -8.862878980874e-01	err = 3.8581370951e-10	time = 0.05 sec
[ Info: VUMPS 231:	obj = -8.862878980874e-01	err = 1.3190179067e-10	time = 0.09 sec
[ Info: VUMPS 232:	obj = -8.862878980874e-01	err = 9.8345519722e-11	time = 0.11 sec
[ Info: VUMPS 233:	obj = -8.862878980874e-01	err = 9.8692106436e-11	time = 0.06 sec
[ Info: VUMPS 234:	obj = -8.862878980874e-01	err = 5.0517584685e-11	time = 0.05 sec
[ Info: VUMPS 235:	obj = -8.862878980874e-01	err = 5.2479684150e-11	time = 0.04 sec
[ Info: VUMPS 236:	obj = -8.862878980874e-01	err = 1.0842073163e-10	time = 0.11 sec
[ Info: VUMPS 237:	obj = -8.862878980874e-01	err = 9.0981410086e-11	time = 0.06 sec
[ Info: VUMPS 238:	obj = -8.862878980874e-01	err = 1.2392458729e-10	time = 0.05 sec
[ Info: VUMPS 239:	obj = -8.862878980874e-01	err = 1.4216588231e-10	time = 0.06 sec
[ Info: VUMPS 240:	obj = -8.862878980874e-01	err = 1.0202004549e-10	time = 0.12 sec
[ Info: VUMPS 241:	obj = -8.862878980874e-01	err = 9.2663307948e-11	time = 0.07 sec
[ Info: VUMPS 242:	obj = -8.862878980874e-01	err = 7.1213927824e-11	time = 0.06 sec
[ Info: VUMPS 243:	obj = -8.862878980874e-01	err = 7.0990626515e-11	time = 0.06 sec
[ Info: VUMPS 244:	obj = -8.862878980874e-01	err = 7.1367091900e-11	time = 0.04 sec
[ Info: VUMPS 245:	obj = -8.862878980874e-01	err = 1.8669503143e-10	time = 0.09 sec
[ Info: VUMPS 246:	obj = -8.862878980874e-01	err = 1.5282765127e-10	time = 0.08 sec
[ Info: VUMPS 247:	obj = -8.862878980874e-01	err = 9.6415117857e-11	time = 0.07 sec
[ Info: VUMPS 248:	obj = -8.862878980874e-01	err = 1.4058659748e-10	time = 0.11 sec
[ Info: VUMPS 249:	obj = -8.862878980874e-01	err = 9.7187257969e-11	time = 0.07 sec
[ Info: VUMPS 250:	obj = -8.862878980874e-01	err = 9.7759239537e-11	time = 0.05 sec
[ Info: VUMPS 251:	obj = -8.862878980874e-01	err = 7.9875821567e-11	time = 0.07 sec
[ Info: VUMPS 252:	obj = -8.862878980874e-01	err = 8.0093896508e-11	time = 0.08 sec
[ Info: VUMPS 253:	obj = -8.862878980874e-01	err = 8.0057483179e-11	time = 0.04 sec
[ Info: VUMPS 254:	obj = -8.862878980874e-01	err = 8.0011136205e-11	time = 0.04 sec
[ Info: VUMPS 255:	obj = -8.862878980874e-01	err = 1.7883745718e-10	time = 0.05 sec
[ Info: VUMPS 256:	obj = -8.862878980874e-01	err = 2.8363520443e-10	time = 0.06 sec
[ Info: VUMPS 257:	obj = -8.862878980874e-01	err = 1.4712790190e-10	time = 0.12 sec
[ Info: VUMPS 258:	obj = -8.862878980874e-01	err = 8.0262189893e-11	time = 0.05 sec
[ Info: VUMPS 259:	obj = -8.862878980874e-01	err = 1.3607892547e-10	time = 0.05 sec
[ Info: VUMPS 260:	obj = -8.862878980874e-01	err = 3.5585465386e-11	time = 0.09 sec
[ Info: VUMPS 261:	obj = -8.862878980874e-01	err = 3.5886789540e-11	time = 0.04 sec
[ Info: VUMPS 262:	obj = -8.862878980874e-01	err = 3.5821881811e-11	time = 0.04 sec
[ Info: VUMPS 263:	obj = -8.862878980874e-01	err = 3.5295520311e-11	time = 0.04 sec
[ Info: VUMPS 264:	obj = -8.862878980874e-01	err = 3.5725163978e-11	time = 0.04 sec
[ Info: VUMPS 265:	obj = -8.862878980874e-01	err = 3.5743028152e-11	time = 0.09 sec
[ Info: VUMPS 266:	obj = -8.862878980874e-01	err = 3.5399343199e-11	time = 0.04 sec
[ Info: VUMPS 267:	obj = -8.862878980874e-01	err = 3.5477332519e-11	time = 0.04 sec
[ Info: VUMPS 268:	obj = -8.862878980874e-01	err = 3.5528256597e-11	time = 0.04 sec
[ Info: VUMPS 269:	obj = -8.862878980874e-01	err = 3.5192330992e-11	time = 0.04 sec
[ Info: VUMPS 270:	obj = -8.862878980874e-01	err = 3.5801828668e-11	time = 0.04 sec
[ Info: VUMPS 271:	obj = -8.862878980874e-01	err = 3.4963884022e-11	time = 0.08 sec
[ Info: VUMPS 272:	obj = -8.862878980874e-01	err = 3.5992081275e-11	time = 0.04 sec
[ Info: VUMPS 273:	obj = -8.862878980874e-01	err = 3.5473635188e-11	time = 0.04 sec
[ Info: VUMPS 274:	obj = -8.862878980874e-01	err = 3.5704579427e-11	time = 0.04 sec
[ Info: VUMPS 275:	obj = -8.862878980874e-01	err = 3.5442668182e-11	time = 0.04 sec
[ Info: VUMPS 276:	obj = -8.862878980874e-01	err = 3.5482076714e-11	time = 0.08 sec
[ Info: VUMPS 277:	obj = -8.862878980874e-01	err = 3.9356745202e-11	time = 0.04 sec
[ Info: VUMPS 278:	obj = -8.862878980874e-01	err = 4.0210942413e-11	time = 0.04 sec
[ Info: VUMPS 279:	obj = -8.862878980874e-01	err = 3.5167580179e-11	time = 0.04 sec
[ Info: VUMPS 280:	obj = -8.862878980874e-01	err = 3.6493383635e-11	time = 0.04 sec
[ Info: VUMPS 281:	obj = -8.862878980874e-01	err = 3.5805399155e-11	time = 0.08 sec
[ Info: VUMPS 282:	obj = -8.862878980874e-01	err = 3.5166101177e-11	time = 0.04 sec
[ Info: VUMPS 283:	obj = -8.862878980874e-01	err = 3.7246847607e-11	time = 0.04 sec
[ Info: VUMPS 284:	obj = -8.862878980874e-01	err = 4.0568537077e-11	time = 0.04 sec
[ Info: VUMPS 285:	obj = -8.862878980874e-01	err = 3.5491580364e-11	time = 0.04 sec
[ Info: VUMPS 286:	obj = -8.862878980874e-01	err = 3.5099655639e-11	time = 0.08 sec
[ Info: VUMPS 287:	obj = -8.862878980874e-01	err = 3.5165898259e-11	time = 0.04 sec
[ Info: VUMPS 288:	obj = -8.862878980874e-01	err = 3.5582900108e-11	time = 0.04 sec
[ Info: VUMPS 289:	obj = -8.862878980874e-01	err = 3.5267676837e-11	time = 0.04 sec
[ Info: VUMPS 290:	obj = -8.862878980874e-01	err = 3.5547016549e-11	time = 0.08 sec
[ Info: VUMPS 291:	obj = -8.862878980874e-01	err = 3.5194773385e-11	time = 0.04 sec
[ Info: VUMPS 292:	obj = -8.862878980874e-01	err = 3.8861800688e-11	time = 0.04 sec
[ Info: VUMPS 293:	obj = -8.862878980874e-01	err = 1.7694618399e-10	time = 0.06 sec
[ Info: VUMPS 294:	obj = -8.862878980874e-01	err = 9.6879691257e-11	time = 0.08 sec
[ Info: VUMPS 295:	obj = -8.862878980874e-01	err = 1.9734638828e-10	time = 0.09 sec
[ Info: VUMPS 296:	obj = -8.862878980874e-01	err = 9.5735210562e-11	time = 0.07 sec
[ Info: VUMPS 297:	obj = -8.862878980874e-01	err = 9.8202831809e-11	time = 0.06 sec
[ Info: VUMPS 298:	obj = -8.862878980874e-01	err = 1.0619064963e-10	time = 0.05 sec
[ Info: VUMPS 299:	obj = -8.862878980874e-01	err = 6.3326732099e-11	time = 0.09 sec
[ Info: VUMPS 300:	obj = -8.862878980874e-01	err = 6.3186774093e-11	time = 0.04 sec
[ Info: VUMPS 301:	obj = -8.862878980874e-01	err = 6.3238257167e-11	time = 0.04 sec
[ Info: VUMPS 302:	obj = -8.862878980874e-01	err = 7.8177257008e-11	time = 0.06 sec
[ Info: VUMPS 303:	obj = -8.862878980874e-01	err = 7.8085760822e-11	time = 0.08 sec
[ Info: VUMPS 304:	obj = -8.862878980874e-01	err = 7.3527317393e-11	time = 0.04 sec
[ Info: VUMPS 305:	obj = -8.862878980874e-01	err = 9.9416857299e-11	time = 0.04 sec
[ Info: VUMPS 306:	obj = -8.862878980874e-01	err = 5.4494619202e-11	time = 0.05 sec
[ Info: VUMPS 307:	obj = -8.862878980874e-01	err = 5.7062728379e-11	time = 0.04 sec
[ Info: VUMPS 308:	obj = -8.862878980874e-01	err = 5.4603016721e-11	time = 0.08 sec
[ Info: VUMPS 309:	obj = -8.862878980874e-01	err = 5.4567688376e-11	time = 0.04 sec
[ Info: VUMPS 310:	obj = -8.862878980874e-01	err = 5.7938510837e-11	time = 0.04 sec
[ Info: VUMPS 311:	obj = -8.862878980874e-01	err = 2.0622949240e-10	time = 0.06 sec
[ Info: VUMPS 312:	obj = -8.862878980874e-01	err = 1.3121811134e-10	time = 0.08 sec
[ Info: VUMPS 313:	obj = -8.862878980874e-01	err = 9.1235627109e-11	time = 0.10 sec
[ Info: VUMPS 314:	obj = -8.862878980874e-01	err = 8.4669915126e-11	time = 0.06 sec
[ Info: VUMPS 315:	obj = -8.862878980874e-01	err = 2.3252823264e-10	time = 0.05 sec
[ Info: VUMPS 316:	obj = -8.862878980874e-01	err = 1.1096003071e-10	time = 0.13 sec
[ Info: VUMPS 317:	obj = -8.862878980874e-01	err = 1.0920664731e-10	time = 0.06 sec
[ Info: VUMPS 318:	obj = -8.862878980874e-01	err = 8.8285347864e-11	time = 0.06 sec
[ Info: VUMPS 319:	obj = -8.862878980874e-01	err = 2.0864332560e-10	time = 0.06 sec
[ Info: VUMPS 320:	obj = -8.862878980874e-01	err = 1.3027532605e-10	time = 0.13 sec
[ Info: VUMPS 321:	obj = -8.862878980874e-01	err = 9.1835678484e-11	time = 0.06 sec
[ Info: VUMPS 322:	obj = -8.862878980874e-01	err = 1.0506692631e-10	time = 0.07 sec
[ Info: VUMPS 323:	obj = -8.862878980874e-01	err = 6.5764134932e-11	time = 0.05 sec
[ Info: VUMPS 324:	obj = -8.862878980874e-01	err = 8.5615212507e-11	time = 0.10 sec
[ Info: VUMPS 325:	obj = -8.862878980874e-01	err = 1.5884913185e-10	time = 0.05 sec
[ Info: VUMPS 326:	obj = -8.862878980874e-01	err = 7.5397480867e-11	time = 0.05 sec
[ Info: VUMPS 327:	obj = -8.862878980874e-01	err = 1.3672488066e-10	time = 0.06 sec
[ Info: VUMPS 328:	obj = -8.862878980874e-01	err = 1.2905960387e-10	time = 0.11 sec
[ Info: VUMPS 329:	obj = -8.862878980874e-01	err = 1.1137546210e-10	time = 0.07 sec
[ Info: VUMPS 330:	obj = -8.862878980874e-01	err = 7.6064748012e-11	time = 0.05 sec
[ Info: VUMPS 331:	obj = -8.862878980874e-01	err = 8.2230706651e-11	time = 0.06 sec
[ Info: VUMPS 332:	obj = -8.862878980874e-01	err = 1.5547070838e-10	time = 0.09 sec
[ Info: VUMPS 333:	obj = -8.862878980874e-01	err = 8.4530602671e-11	time = 0.05 sec
[ Info: VUMPS 334:	obj = -8.862878980874e-01	err = 2.7703069729e-10	time = 0.05 sec
[ Info: VUMPS 335:	obj = -8.862878980874e-01	err = 1.2843108098e-10	time = 0.07 sec
[ Info: VUMPS 336:	obj = -8.862878980874e-01	err = 7.7139997032e-11	time = 0.09 sec
[ Info: VUMPS 337:	obj = -8.862878980874e-01	err = 1.5230480609e-10	time = 0.05 sec
[ Info: VUMPS 338:	obj = -8.862878980874e-01	err = 1.4349332630e-10	time = 0.05 sec
[ Info: VUMPS 339:	obj = -8.862878980874e-01	err = 1.8791131229e-10	time = 0.07 sec
[ Info: VUMPS 340:	obj = -8.862878980874e-01	err = 5.6705763103e-11	time = 0.11 sec
[ Info: VUMPS 341:	obj = -8.862878980874e-01	err = 5.6628206369e-11	time = 0.04 sec
[ Info: VUMPS 342:	obj = -8.862878980874e-01	err = 5.7700869354e-11	time = 0.04 sec
[ Info: VUMPS 343:	obj = -8.862878980874e-01	err = 9.5014822831e-11	time = 0.07 sec
[ Info: VUMPS 344:	obj = -8.862878980874e-01	err = 9.9584310546e-11	time = 0.09 sec
[ Info: VUMPS 345:	obj = -8.862878980874e-01	err = 1.0944426167e-10	time = 0.04 sec
[ Info: VUMPS 346:	obj = -8.862878980874e-01	err = 4.1610580123e-11	time = 0.04 sec
[ Info: VUMPS 347:	obj = -8.862878980874e-01	err = 2.9414073597e-11	time = 0.04 sec
[ Info: VUMPS 348:	obj = -8.862878980874e-01	err = 2.9723554637e-11	time = 0.04 sec
[ Info: VUMPS 349:	obj = -8.862878980874e-01	err = 2.9370382842e-11	time = 0.08 sec
[ Info: VUMPS 350:	obj = -8.862878980874e-01	err = 2.9069190284e-11	time = 0.04 sec
[ Info: VUMPS 351:	obj = -8.862878980874e-01	err = 2.9200689531e-11	time = 0.04 sec
[ Info: VUMPS 352:	obj = -8.862878980874e-01	err = 1.0829490368e-10	time = 0.06 sec
[ Info: VUMPS 353:	obj = -8.862878980874e-01	err = 1.0018375647e-10	time = 0.11 sec
[ Info: VUMPS 354:	obj = -8.862878980874e-01	err = 1.5362554440e-10	time = 0.06 sec
[ Info: VUMPS 355:	obj = -8.862878980874e-01	err = 9.4013179693e-11	time = 0.07 sec
[ Info: VUMPS 356:	obj = -8.862878980874e-01	err = 8.5844015408e-11	time = 0.06 sec
[ Info: VUMPS 357:	obj = -8.862878980874e-01	err = 1.1938734236e-10	time = 0.09 sec
[ Info: VUMPS 358:	obj = -8.862878980874e-01	err = 5.4442781639e-11	time = 0.04 sec
[ Info: VUMPS 359:	obj = -8.862878980874e-01	err = 5.6747362650e-11	time = 0.04 sec
[ Info: VUMPS 360:	obj = -8.862878980874e-01	err = 1.1602629725e-10	time = 0.07 sec
[ Info: VUMPS 361:	obj = -8.862878980874e-01	err = 1.2693714656e-10	time = 0.06 sec
[ Info: VUMPS 362:	obj = -8.862878980874e-01	err = 1.3334525033e-10	time = 0.11 sec
[ Info: VUMPS 363:	obj = -8.862878980874e-01	err = 9.4883693020e-11	time = 0.07 sec
[ Info: VUMPS 364:	obj = -8.862878980874e-01	err = 8.9430760837e-11	time = 0.07 sec
[ Info: VUMPS 365:	obj = -8.862878980874e-01	err = 1.0615371329e-10	time = 0.11 sec
[ Info: VUMPS 366:	obj = -8.862878980874e-01	err = 1.1358908029e-10	time = 0.04 sec
[ Info: VUMPS 367:	obj = -8.862878980874e-01	err = 1.2828241179e-10	time = 0.05 sec
[ Info: VUMPS 368:	obj = -8.862878980874e-01	err = 7.5500082303e-11	time = 0.05 sec
[ Info: VUMPS 369:	obj = -8.862878980874e-01	err = 1.7133532560e-10	time = 0.05 sec
[ Info: VUMPS 370:	obj = -8.862878980874e-01	err = 6.2722200745e-11	time = 0.09 sec
[ Info: VUMPS 371:	obj = -8.862878980874e-01	err = 6.2778165324e-11	time = 0.04 sec
[ Info: VUMPS 372:	obj = -8.862878980874e-01	err = 6.4224600150e-10	time = 0.06 sec
[ Info: VUMPS 373:	obj = -8.862878980874e-01	err = 1.4567170198e-10	time = 0.09 sec
[ Info: VUMPS 374:	obj = -8.862878980874e-01	err = 1.0380674404e-10	time = 0.11 sec
[ Info: VUMPS 375:	obj = -8.862878980874e-01	err = 1.0822040195e-10	time = 0.07 sec
[ Info: VUMPS 376:	obj = -8.862878980874e-01	err = 1.0520173008e-10	time = 0.06 sec
[ Info: VUMPS 377:	obj = -8.862878980874e-01	err = 6.7365662418e-11	time = 0.10 sec
[ Info: VUMPS 378:	obj = -8.862878980874e-01	err = 6.7760750536e-11	time = 0.04 sec
[ Info: VUMPS 379:	obj = -8.862878980874e-01	err = 6.7722699479e-11	time = 0.04 sec
[ Info: VUMPS 380:	obj = -8.862878980874e-01	err = 6.7250908434e-11	time = 0.04 sec
[ Info: VUMPS 381:	obj = -8.862878980874e-01	err = 1.4694592798e-10	time = 0.06 sec
[ Info: VUMPS 382:	obj = -8.862878980874e-01	err = 8.9730375422e-11	time = 0.11 sec
[ Info: VUMPS 383:	obj = -8.862878980874e-01	err = 1.6221755374e-10	time = 0.06 sec
[ Info: VUMPS 384:	obj = -8.862878980874e-01	err = 1.2999407274e-10	time = 0.08 sec
[ Info: VUMPS 385:	obj = -8.862878980874e-01	err = 8.5732018525e-11	time = 0.06 sec
[ Info: VUMPS 386:	obj = -8.862878980874e-01	err = 1.6277251600e-10	time = 0.09 sec
[ Info: VUMPS 387:	obj = -8.862878980874e-01	err = 7.1550742938e-11	time = 0.04 sec
[ Info: VUMPS 388:	obj = -8.862878980874e-01	err = 7.4376591685e-11	time = 0.06 sec
[ Info: VUMPS 389:	obj = -8.862878980874e-01	err = 7.4713904887e-11	time = 0.04 sec
[ Info: VUMPS 390:	obj = -8.862878980874e-01	err = 7.4436898750e-11	time = 0.08 sec
[ Info: VUMPS 391:	obj = -8.862878980874e-01	err = 7.5772899650e-11	time = 0.04 sec
[ Info: VUMPS 392:	obj = -8.862878980874e-01	err = 7.4943197420e-11	time = 0.04 sec
[ Info: VUMPS 393:	obj = -8.862878980874e-01	err = 7.4400646683e-11	time = 0.04 sec
[ Info: VUMPS 394:	obj = -8.862878980874e-01	err = 7.5613615370e-11	time = 0.04 sec
[ Info: VUMPS 395:	obj = -8.862878980874e-01	err = 1.0859523215e-10	time = 0.11 sec
[ Info: VUMPS 396:	obj = -8.862878980874e-01	err = 9.0566692582e-11	time = 0.05 sec
[ Info: VUMPS 397:	obj = -8.862878980874e-01	err = 4.3667065720e-11	time = 0.05 sec
[ Info: VUMPS 398:	obj = -8.862878980874e-01	err = 4.3513888787e-11	time = 0.04 sec
[ Info: VUMPS 399:	obj = -8.862878980874e-01	err = 4.4283893567e-11	time = 0.04 sec
┌ Warning: VUMPS cancel 400:	obj = -8.862878980874e-01	err = 4.3759074890e-11	time = 28.78 sec
└ @ MPSKit ~/Projects/MPSKit.jl/src/algorithms/groundstate/vumps.jl:67

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