MPSKit.jl

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Entanglement entropy and spectrum ​

The examples on this page use MPSKit.jl, TensorKit.jl, and TensorKitTensors.jl. See Installation for how to add these packages to your environment.

This page collects recipes for extracting the entanglement entropy and the entanglement spectrum from the gauge (bond) tensors of an MPS. For general expectation values and correlators see Computing observables; for building the state objects used below see Constructing states. The reference page for these and related functions is Observables and analysis.

julia
using MPSKit, TensorKit
using TensorKitTensors.SpinOperators: σˣ, σᶻ

Setup: a TFIM ground state ​

The examples below reuse a spin-1/2 FiniteMPS and the transverse-field Ising Hamiltonian, optimized with DMRG so the entanglement structure reflects an actual ground state rather than a random tensor:

julia
L = 8
ψ0 = FiniteMPS(L, ℂ^2, ℂ^8)

# single-site Pauli operators
X = σˣ()
Z = σᶻ()

lattice = fill(ℂ^2, L)
H = FiniteMPOHamiltonian(lattice, (i, i + 1) => -(X ⊗ X) for i in 1:(L - 1)) +
    FiniteMPOHamiltonian(lattice, (i,) => -0.5 * Z for i in 1:L)

ψ, envs, _ = find_groundstate(ψ0, H, DMRG(; maxiter = 10))
(FiniteMPS{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 1, 1, Vector{ComplexF64}}}(Union{Missing, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.819362926690691 + 0.5732676237164038im, 0.0023644017885220865 + 0.0017422880345984622im, -0.0012324179090753343 - 0.002665916260962034im, 0.3971970258834747 + 0.9177286617873005im], (ℂ^1 ⊗ ℂ^2) ← ℂ^2), missing, missing, missing, missing, missing, missing, missing], Union{Missing, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}}[missing, TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.5880582148396138 + 0.581783625730926im, 0.03224154883974908 + 0.007706554583574388im, 0.019406960013375395 + 0.019425275076849335im, 0.6572788365325448 + 0.15264390961221705im, -0.03134581168034833 - 0.02072429888351857im, 0.735720947747839 + 0.028651404008604577im, 0.4650040291587172 + 0.3118633663757274im, -0.0326375441975668 - 0.001067042411830021im, -0.00024171397350953693 + 0.00029347353520769564im, 0.002883469646542458 + 0.014921731504372331im, 0.0024286131509286997 - 0.0064312211225271265im, 0.00020715486424591873 - 0.0012394967488463656im, -0.0017310872527346213 - 0.003319089646630492im, 0.0014244087759874788 + 0.0002683058237728496im, -0.0004724581784212062 - 0.0004182485897966476im, 0.011465192002799779 + 0.006840495781039323im], (ℂ^2 ⊗ ℂ^2) ← ℂ^4), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.6472000169271117 + 0.4873502331120741im, 0.06245126834141456 + 0.06895203797808414im, 0.12738851120818093 - 0.09092726028057475im, -0.5085422517149275 - 0.17369013807947406im, 0.10283481831204631 + 0.07743834488649072im, 0.42405281628808816 + 0.4680415813542904im, -0.6466421544840285 + 0.363621906524926im, 0.074775733329564 + 0.000991003442695456im, -0.07010414810573203 - 0.07799838368171524im, 0.3907884077881596 + 0.6484205963195792im  …  1.343145651084602e-5 + 0.00013196097002151467im, 2.4873765769248446e-6 - 6.2361526580898e-6im, 9.938768927102522e-10 + 2.406963719297858e-10im, -1.9457952764955133e-8 - 1.4577791435468765e-8im, -6.233646942806156e-5 + 5.1305052494057655e-5im, -2.404581014440057e-5 - 4.382031769797086e-6im, 9.570623339816685e-9 + 4.688707021750244e-9im, -2.8406662976292246e-9 - 1.7584306635867163e-9im, 1.14869771260665e-6 + 4.657298753391952e-6im, 0.00017406313959800364 + 2.561998385419416e-5im], (ℂ^4 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.4270155702673373 + 0.6886235649388642im, 0.04860476109538264 + 0.05189781788627887im, 0.12154272708823806 - 0.2384349247871924im, 0.38412641820206667 - 0.30940539980410914im, 0.019725751532827542 + 0.06495502223491703im, -0.09507588241848404 - 0.09571420918483392im, 0.007555105598674972 - 0.010922090422814978im, -0.0008138331554164935 - 0.0017396850136206785im, 0.13786409064097052 + 0.22194336870974424im, 0.3963719208608296 + 0.42658349025804004im  …  -0.0007423535373013506 + 0.0015388425191365865im, 0.02255856136445944 + 0.008714465133841711im, 2.1163919016593548e-8 + 4.279101772065111e-9im, -5.594051757963568e-9 + 2.1637372433251874e-9im, 2.5600586297593515e-6 + 2.731032033102659e-5im, -8.924994025897006e-6 + 0.00017206074584654452im, 0.0002131803900716798 + 0.000319653932830881im, -0.0026063497962091468 + 0.00017610682833195894im, 0.0047338735038555116 + 0.021251028585003533im, -0.0034386937232605205 - 0.0002772641496965229im], (ℂ^8 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.6626297921648145 - 0.48511223318940205im, -0.07864857299784932 + 0.022213478895608964im, 0.2595706393456464 + 0.05296112635482544im, 0.30491069444698926 - 0.36829895100538834im, -0.06177626212307563 + 0.026928619949897724im, -0.03820930847170658 + 0.117110270191088im, 0.010153897809774501 - 0.006656208446844568im, 0.0007897021274520971 + 0.0017086170977224156im, -0.2266081837971145 - 0.1659042477909343im, 0.5693877121992168 - 0.16077981225667662im  …  -0.003202463630476399 + 0.004375369026415265im, -0.003721955915854114 - 0.015859308429362347im, -1.5144988614547404e-8 - 8.37121757888068e-9im, 2.54185503597349e-9 - 1.9947530394504045e-9im, -5.439138121879164e-5 - 1.9102959997209273e-6im, -5.4122883160396385e-5 + 8.125657485443667e-5im, -0.0007282543764506064 + 0.0004745450082203836im, -0.00032944641260052547 + 0.001535962485956999im, -0.011591322355382006 + 0.009736713543995516im, -0.0020020578284012727 - 0.003224663821235365im], (ℂ^8 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.6753549269707955 - 0.5063461330837814im, -0.10669263684671548 - 0.06313194274853096im, 0.03184092288650954 - 0.13457326991373839im, 0.4295906328859077 - 0.2398145527867901im, 0.021023845064041022 + 0.01104353369978734im, 0.10149615786579758 - 0.0027955923163576896im, -0.007039534513503309 + 0.005221315113138968im, 0.0017876420601241855 + 0.0020382100222505724im, -0.13219525868479287 - 0.09910941730469867im, 0.5848886719322459 + 0.3460690620448651im  …  0.5856467983686291 + 0.35581267195708416im, 0.06801805353974764 - 0.12312346013541021im, 0.00031817447256440385 - 0.001270175019188986im, -0.0013615428404415795 + 0.008977272114165163im, 0.09964195024949181 - 0.014737178319740973im, -0.020643099488919483 - 0.01713716250100361im, -0.37751612333719564 - 0.32531561500143663im, 0.11081055352906008 + 0.018684712784026173im, -0.21240300425731046 - 0.10278428267277938im, 0.2965607879963219 - 0.7644904196063075im], (ℂ^8 ⊗ ℂ^2) ← ℂ^4), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.5682951665046909 - 0.698685050652833im, -0.02155446746811754 + 0.04628417608924896im, 0.023109491795230242 + 0.0050954625848776865im, 0.4118644036621465 - 0.1268096382125406im, -0.030056074866312264 - 0.036947231845553465im, 0.3336774308726312 - 0.7166144152273848im, -0.5999113734457753 - 0.11044568062240068im, 0.02602793576605155 - 0.00923735022353097im, 0.017066619050362723 - 0.028411931841759462im, 0.6073199878920219 + 0.05402417409992418im, 0.12990635634401276 + 0.7801490628932527im, -0.025539754962438016 - 0.03138172601253128im, 0.22177598252442227 - 0.36922654883251704im, -0.02746256109825522 - 0.002441443843151589im, -0.005339972179506198 - 0.04255991350549555im, -0.5422474953882119 - 0.719621295201288im], (ℂ^4 ⊗ ℂ^2) ← ℂ^2), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.8922772890373167 + 0.45147846557887483im, -0.0021183607928111654 + 0.0019867396188600252im, 0.0025939757223096323 + 0.0013060921536154505im, 0.7280501430618351 - 0.6855177274154771im], (ℂ^2 ⊗ ℂ^2) ← ℂ^1)], Union{Missing, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.7067893542260827 + 0.49450547537183487im, 0.0007014535097524955 + 0.0005168893302380524im, -0.000623452904174803 - 0.0013486279475041403im, 0.20093317168884922 + 0.46425858892705646im], (ℂ^1 ⊗ ℂ^2) ← ℂ^2), missing, missing, missing, missing, missing, missing, missing], Union{Missing, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 1, 1, Vector{ComplexF64}}}[missing, TensorMap{ComplexF64, TensorKit.ComplexSpace, 1, 1, Vector{ComplexF64}}(ComplexF64[0.8626035317016973 + 0.0im, -0.0014363906448198321 + 0.0008363667423924013im, 0.0 - 0.0im, 0.5058778354191322 + 0.0im], ℂ^2 ← ℂ^2), missing, missing, missing, missing, missing, missing, missing]), MPSKit.FiniteEnvironments{Nothing, FiniteMPOHamiltonian{JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}}(nothing, JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}[JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), (⊞(ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 3) => 1.0 + 0.0im, CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 3) => 1.0 + 0.0im, CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 3) => 1.0 + 0.0im, CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 3) => 1.0 + 0.0im, CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 3) => 1.0 + 0.0im, CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 3) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 2) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, 0.7071067811865475 + 0.0im, 0.7071067811865472 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 3) => 1.0 + 0.0im, CartesianIndex(1, 1, 1, 1) => 1.0 + 0.0im)), JordanMPOTensor{ComplexF64, TensorKit.ComplexSpace, Vector{ComplexF64}}(BlockTensorKit.SparseBlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 2, 4}(Dict{CartesianIndex{4}, TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}}(CartesianIndex(2, 1, 1, 1) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im, -1.414213562373095 + 0.0im, -1.4142135623730951 + 0.0im, 0.0 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1)), CartesianIndex(1, 1, 1, 1) => TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 2, Vector{ComplexF64}}(ComplexF64[-0.5 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.5 + 0.0im], (ℂ^1 ⊗ ℂ^2) ← (ℂ^2 ⊗ ℂ^1))), ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞(ℂ^2)) ← (⊞(ℂ^2) ⊗ ⊞(ℂ^1))), Dict{CartesianIndex{4}, ComplexF64}(CartesianIndex(3, 1, 1, 1) => 1.0 + 0.0im))], TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.819362926690691 + 0.5732676237164038im, 0.0023644017885220865 + 0.0017422880345984622im, -0.0012324179090753343 - 0.002665916260962034im, 0.3971970258834747 + 0.9177286617873005im], (ℂ^1 ⊗ ℂ^2) ← ℂ^2), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.6401613240436124 + 0.6333297134337772im, 0.033534729387925996 + 0.007994873616981368im, 0.0348995788718452 + 0.03496960522798284im, 0.4194850868860599 + 0.0974159390772745im, -0.04424932755840151 - 0.029255464783186396im, 0.6091825500053785 + 0.023725418874635144im, 0.6564231231924761 + 0.44024204550666973im, -0.02853952299488941 - 0.0009799962649801519im, -0.03532702512436195 + 0.04203698953921297im, 0.1491420019378721 + 0.7715585056332096im, 0.21424642764395707 - 0.5672269155890716im, 0.018140810481329837 - 0.10706088883222512im, -0.19796322734137622 - 0.3795635934840128im, 0.09622653050034076 + 0.018434198104983812im, -0.05402924990426693 - 0.047829963819747925im, 0.7690566296001811 + 0.458789395555277im], (ℂ^2 ⊗ ℂ^2) ← ℂ^4), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.6739650176345686 + 0.5074906244215992im, 0.06090031779227608 + 0.0671340640694055im, 0.002044343875997127 - 0.0013913483905494527im, -0.004906730948788973 - 0.0016283560859179514im, 0.13553234864741262 + 0.10215827280475467im, 0.3364685613692427 + 0.37130575749706407im, -0.00829019902519566 + 0.004684223324640886im, 0.0008198879153200174 - 0.00013031517686198194im, -0.08462371053025121 - 0.09415295415261624im, 0.3658936481568642 + 0.6071540589684914im  …  0.07325316900576473 + 0.7119877723744111im, -0.0012536258917057097 - 0.027121389373655193im, 0.000505050716433851 + 0.00012231280954190255im, -0.00764770126911545 - 0.0057262981863451115im, -0.38924091239012903 + 0.3203586219469257im, -0.138296285761244 - 0.03333499732066636im, 0.004863429474964282 + 0.002382623902268094im, -0.0012208371998238378 - 0.0007710283124488237im, 0.007172689595958702 + 0.029081069760226806im, 0.8420137635183722 + 0.12496993271229317im], (ℂ^4 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.43132384771791465 + 0.6955337352987955im, 0.046755062210511004 + 0.04983906280756141im, 0.0022572830389440725 - 0.004420274649063705im, 0.004998399247262083 - 0.004031807411405704im, 3.6360317570204473e-6 + 1.1411561080004469e-5im, -1.1636252797860643e-5 - 1.1979606988942878e-5im, 1.8134742662612838e-8 - 2.6256019448795477e-8im, -2.0679354478841646e-9 - 4.327639868675673e-9im, 0.15969463297632902 + 0.2571570093585519im, 0.3290751600691394 + 0.3541024893086526im  …  -0.0006049484641927731 + 0.0012540294433197791im, 0.015858078879992465 + 0.006093446150043605im, 0.007212797118682057 + 0.0014583472493807509im, -0.0020329984992165304 + 0.0006380049783805131im, 0.013874942746030558 + 0.14801535828888263im, -0.03938357819541926 + 0.8045439326698494im, 0.01088307471115501 + 0.016319105056455913im, -0.11462200966123995 + 0.008089031048514182im, 0.003857727642018275 + 0.017317921376518483im, -0.0029039273467383058 - 0.00045106552970038913im], (ℂ^8 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.6541394860096381 - 0.47889712794584743im, -0.07677915994022547 + 0.02168660666189291im, 0.0048926409997309 + 0.001000161040488313im, 0.004180180577950413 - 0.005052131633260118im, -1.3807336502050074e-5 + 5.975242221156677e-6im, -6.172504240898872e-6 + 1.904584343231321e-5im, 3.318270143508124e-8 - 2.190943535544179e-8im, 2.9633094939802866e-9 + 6.819867834383453e-9im, -0.24865752716426576 - 0.1820485030565001im, 0.4726426494923108 - 0.13346268659303698im  …  -0.00508378785904735 + 0.006945729884005322im, -0.0052989976381434545 - 0.022232348828213715im, -0.00714624853900377 - 0.003950006362850374im, 0.0006108993040006578 - 0.0006499355166017257im, -0.43067468108981916 - 0.01512585453856347im, -0.37412614264933813 + 0.5587482413206933im, -0.06825217971174675 + 0.04447447516934437im, -0.02708230819290356 + 0.1251936344352896im, -0.018400779466269168 + 0.015456659065353949im, -0.003046690748810221 - 0.004239007606343765im], (ℂ^8 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.6456799398184685 - 0.48409783361516007im, -0.10823981990529885 - 0.06404620061808727im, 0.000577268646321959 - 0.0024300575247444244im, 0.005475900167601154 - 0.003058021923912955im, 3.6716812105837965e-6 + 1.2301059256260764e-6im, 1.235429767081137e-5 - 1.080237711238502e-7im, -1.573637881504773e-8 + 1.164130817047188e-8im, 4.942973916702709e-9 + 5.585546581784997e-9im, -0.14106788013863258 - 0.10576472507473866im, 0.47270864897736053 + 0.2796927701295418im  …  0.00013919602483743044 + 8.456924838091933e-5im, 1.9506648190722928e-5 - 3.566111242163159e-5im, 0.031832894559910827 - 0.12707916864792265im, -0.1177218498187532 + 0.7754883251821523im, 0.1587055990493721 - 0.02347277133451503im, -0.03580289278725978 - 0.029625625151484262im, -0.005654030658149734 - 0.004872227560571975im, 0.0018718984399652037 + 0.0001856935945096646im, -5.048376231493144e-5 - 2.442967955989108e-5im, 6.0342023694771235e-5 - 0.00015581587004385506im], (ℂ^8 ⊗ ℂ^2) ← ℂ^4), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.5211760644965544 - 0.6407554550362196im, -0.024978607968633566 + 0.05364384120896426im, 0.00030971019938251054 + 6.661669636627913e-5im, 0.0035839395211844085 - 0.001103317777370558im, -0.028935630438855393 - 0.035576960998254234im, 0.2358330691111033 - 0.5064822945344135im, -0.0067793680902054395 - 0.0012482192277617403im, 0.00035456321349217686 - 0.0001271484129661071im, 0.026682758664055905 - 0.0444205567767191im, 0.7323110623167017 + 0.06514252574703339im, 0.002502222242847631 + 0.015027027105108783im, -0.0006303090674532197 - 0.0007737752212312267im, 0.3467350505522223 - 0.5772662333287927im, -0.05380060665314752 - 0.004786551007361219im, -0.00010285714679532646 - 0.000819777917188733im, -0.008054594628286811 - 0.01068926172895649im], (ℂ^4 ⊗ ℂ^2) ← ℂ^2), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[6.89997867987706e-310 + 2.130317216e-314im, 5.0e-324 + 6.89996668385133e-310im, 6.89987421453493e-310 + 6.89996668385133e-310im, 6.8999710035325e-310 + 6.89988082084083e-310im], (ℂ^1 ⊗ ℂ^2) ← ℂ^2)], TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[6.89997867987706e-310 + 2.130317216e-314im, 5.0e-324 + 6.89996668385133e-310im, 6.89987421453493e-310 + 6.89996668385133e-310im, 6.8999710035325e-310 + 6.89988082084083e-310im], (ℂ^1 ⊗ ℂ^2) ← ℂ^2), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.5880582148396138 + 0.581783625730926im, 0.03224154883974908 + 0.007706554583574388im, 0.019406960013375395 + 0.019425275076849335im, 0.6572788365325448 + 0.15264390961221705im, -0.03134581168034833 - 0.02072429888351857im, 0.735720947747839 + 0.028651404008604577im, 0.4650040291587172 + 0.3118633663757274im, -0.0326375441975668 - 0.001067042411830021im, -0.00024171397350953693 + 0.00029347353520769564im, 0.002883469646542458 + 0.014921731504372331im, 0.0024286131509286997 - 0.0064312211225271265im, 0.00020715486424591873 - 0.0012394967488463656im, -0.0017310872527346213 - 0.003319089646630492im, 0.0014244087759874788 + 0.0002683058237728496im, -0.0004724581784212062 - 0.0004182485897966476im, 0.011465192002799779 + 0.006840495781039323im], (ℂ^2 ⊗ ℂ^2) ← ℂ^4), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.6472000169271117 + 0.4873502331120741im, 0.06245126834141456 + 0.06895203797808414im, 0.12738851120818093 - 0.09092726028057475im, -0.5085422517149275 - 0.17369013807947406im, 0.10283481831204631 + 0.07743834488649072im, 0.42405281628808816 + 0.4680415813542904im, -0.6466421544840285 + 0.363621906524926im, 0.074775733329564 + 0.000991003442695456im, -0.07010414810573203 - 0.07799838368171524im, 0.3907884077881596 + 0.6484205963195792im  …  1.343145651084602e-5 + 0.00013196097002151467im, 2.4873765769248446e-6 - 6.2361526580898e-6im, 9.938768927102522e-10 + 2.406963719297858e-10im, -1.9457952764955133e-8 - 1.4577791435468765e-8im, -6.233646942806156e-5 + 5.1305052494057655e-5im, -2.404581014440057e-5 - 4.382031769797086e-6im, 9.570623339816685e-9 + 4.688707021750244e-9im, -2.8406662976292246e-9 - 1.7584306635867163e-9im, 1.14869771260665e-6 + 4.657298753391952e-6im, 0.00017406313959800364 + 2.561998385419416e-5im], (ℂ^4 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.4270155702673373 + 0.6886235649388642im, 0.04860476109538264 + 0.05189781788627887im, 0.12154272708823806 - 0.2384349247871924im, 0.38412641820206667 - 0.30940539980410914im, 0.019725751532827542 + 0.06495502223491703im, -0.09507588241848404 - 0.09571420918483392im, 0.007555105598674972 - 0.010922090422814978im, -0.0008138331554164935 - 0.0017396850136206785im, 0.13786409064097052 + 0.22194336870974424im, 0.3963719208608296 + 0.42658349025804004im  …  -0.0007423535373013506 + 0.0015388425191365865im, 0.02255856136445944 + 0.008714465133841711im, 2.1163919016593548e-8 + 4.279101772065111e-9im, -5.594051757963568e-9 + 2.1637372433251874e-9im, 2.5600586297593515e-6 + 2.731032033102659e-5im, -8.924994025897006e-6 + 0.00017206074584654452im, 0.0002131803900716798 + 0.000319653932830881im, -0.0026063497962091468 + 0.00017610682833195894im, 0.0047338735038555116 + 0.021251028585003533im, -0.0034386937232605205 - 0.0002772641496965229im], (ℂ^8 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.6626297921648145 - 0.48511223318940205im, -0.07864857299784932 + 0.022213478895608964im, 0.2595706393456464 + 0.05296112635482544im, 0.30491069444698926 - 0.36829895100538834im, -0.06177626212307563 + 0.026928619949897724im, -0.03820930847170658 + 0.117110270191088im, 0.010153897809774501 - 0.006656208446844568im, 0.0007897021274520971 + 0.0017086170977224156im, -0.2266081837971145 - 0.1659042477909343im, 0.5693877121992168 - 0.16077981225667662im  …  -0.003202463630476399 + 0.004375369026415265im, -0.003721955915854114 - 0.015859308429362347im, -1.5144988614547404e-8 - 8.37121757888068e-9im, 2.54185503597349e-9 - 1.9947530394504045e-9im, -5.439138121879164e-5 - 1.9102959997209273e-6im, -5.4122883160396385e-5 + 8.125657485443667e-5im, -0.0007282543764506064 + 0.0004745450082203836im, -0.00032944641260052547 + 0.001535962485956999im, -0.011591322355382006 + 0.009736713543995516im, -0.0020020578284012727 - 0.003224663821235365im], (ℂ^8 ⊗ ℂ^2) ← ℂ^8), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.6753549269707955 - 0.5063461330837814im, -0.10669263684671548 - 0.06313194274853096im, 0.03184092288650954 - 0.13457326991373839im, 0.4295906328859077 - 0.2398145527867901im, 0.021023845064041022 + 0.01104353369978734im, 0.10149615786579758 - 0.0027955923163576896im, -0.007039534513503309 + 0.005221315113138968im, 0.0017876420601241855 + 0.0020382100222505724im, -0.13219525868479287 - 0.09910941730469867im, 0.5848886719322459 + 0.3460690620448651im  …  0.5856467983686291 + 0.35581267195708416im, 0.06801805353974764 - 0.12312346013541021im, 0.00031817447256440385 - 0.001270175019188986im, -0.0013615428404415795 + 0.008977272114165163im, 0.09964195024949181 - 0.014737178319740973im, -0.020643099488919483 - 0.01713716250100361im, -0.37751612333719564 - 0.32531561500143663im, 0.11081055352906008 + 0.018684712784026173im, -0.21240300425731046 - 0.10278428267277938im, 0.2965607879963219 - 0.7644904196063075im], (ℂ^8 ⊗ ℂ^2) ← ℂ^4), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.5682951665046909 - 0.698685050652833im, -0.02155446746811754 + 0.04628417608924896im, 0.023109491795230242 + 0.0050954625848776865im, 0.4118644036621465 - 0.1268096382125406im, -0.030056074866312264 - 0.036947231845553465im, 0.3336774308726312 - 0.7166144152273848im, -0.5999113734457753 - 0.11044568062240068im, 0.02602793576605155 - 0.00923735022353097im, 0.017066619050362723 - 0.028411931841759462im, 0.6073199878920219 + 0.05402417409992418im, 0.12990635634401276 + 0.7801490628932527im, -0.025539754962438016 - 0.03138172601253128im, 0.22177598252442227 - 0.36922654883251704im, -0.02746256109825522 - 0.002441443843151589im, -0.005339972179506198 - 0.04255991350549555im, -0.5422474953882119 - 0.719621295201288im], (ℂ^4 ⊗ ℂ^2) ← ℂ^2), TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.8922772890373167 + 0.45147846557887483im, -0.0021183607928111654 + 0.0019867396188600252im, 0.0025939757223096323 + 0.0013060921536154505im, 0.7280501430618351 - 0.6855177274154771im], (ℂ^2 ⊗ ℂ^2) ← ℂ^1)], BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}[BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0 + 0.0im], (ℂ^1 ⊗ (ℂ^1)') ← ℂ^1);;;], (⊞(ℂ^1) ⊗ ⊞((ℂ^1)')) ← ⊞(ℂ^1)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0 + 0.0im, 0.0 - 8.673617379884035e-19im, 0.0 + 8.673617379884035e-19im, 1.0000000000000002 + 0.0im], (ℂ^2 ⊗ (ℂ^1)') ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.004152273134494729 + 0.0im, 0.6021333062355393 - 0.3706996630018361im, 0.6021333062355391 + 0.370699663001836im, -0.0041522731344947285 + 0.0im], (ℂ^2 ⊗ (ℂ^1)') ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.49999137403658694 + 0.0im, 0.0025380810248346137 - 0.0014778476637330004im, 0.0025380810248346137 + 0.0014778476637330004im, 0.499991374036587 + 0.0im], (ℂ^2 ⊗ (ℂ^1)') ← ℂ^2);;;], (⊞(ℂ^2) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^2)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999999 + 0.0im, 2.1250362580715887e-17 + 5.637851296924623e-18im, 1.734723475976807e-18 - 1.734723475976807e-17im, 1.3877787807814457e-16 - 6.938893903907228e-17im, 2.0816681711721685e-17 - 5.204170427930421e-18im, 1.0 + 0.0im, 2.7755575615628914e-17 - 2.914335439641036e-16im, 3.469446951953614e-17 - 3.469446951953614e-18im, 2.168404344971009e-18 + 1.734723475976807e-17im, 2.7755575615628914e-17 + 2.3592239273284576e-16im, 0.9999999999999999 - 1.3877787807814457e-17im, 3.469446951953614e-17 - 8.673617379884035e-18im, 1.3877787807814457e-16 + 6.938893903907228e-17im, 2.0816681711721685e-17 + 3.469446951953614e-18im, 2.7755575615628914e-17 + 5.204170427930421e-18im, 0.9999999999999999 + 0.0im], (ℂ^4 ⊗ (ℂ^1)') ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.0839120755845771 + 6.938893903907228e-18im, 0.6741252406024228 + 0.12910092881577512im, -0.059662073543725797 + 0.1348521429038786im, -0.009505033513471511 - 0.003444503639170914im, 0.6741252406024228 - 0.12910092881577512im, -0.08391207558458365 + 3.469446951953614e-18im, 0.004192885473790112 + 0.009199455354348048im, 0.12965444717215846 - 0.07024519765639176im, -0.05966207354372577 - 0.1348521429038785im, 0.004192885473790108 - 0.009199455354348034im, -0.1574180681304886 + 3.469446951953614e-18im, 0.45342330576956347 + 0.4977750334019852im, -0.009505033513471501 + 0.0034445036391709104im, 0.12965444717215818 + 0.07024519765639164im, 0.4534233057695634 - 0.49777503340198515im, 0.1574180681304952 + 6.938893903907228e-18im], (ℂ^4 ⊗ (ℂ^1)') ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-1.404486898297137 - 1.1102230246251565e-16im, 0.026123744769065108 + 0.0051990230638772564im, -0.007553400370650128 + 0.032377179530096695im, 0.14075870418276815 - 0.04575372647566822im, 0.0261237447690651 - 0.005199023063877246im, -0.968748077465818 - 5.551115123125783e-17im, -0.05752905589024537 + 0.24418805778072503im, -0.03867745915278625 + 0.00892510912223268im, -0.007553400370650113 - 0.032377179530096646im, -0.057529055890245345 - 0.24418805778072422im, 0.9736856138869765 + 5.551115123125783e-17im, -0.01952785288057798 - 0.049550377148005295im, 0.1407587041827683 + 0.04575372647566821im, -0.0386774591527862 - 0.00892510912223267im, -0.019527852880577967 + 0.04955037714800531im, 1.3995493618759787 - 1.1102230246251565e-16im], (ℂ^4 ⊗ (ℂ^1)') ← ℂ^4);;;], (⊞(ℂ^4) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^4)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0 + 9.634803668440695e-18im, 5.735788056659431e-18 + 2.533088069258307e-17im, 3.724653210067363e-18 - 4.4819777798429554e-17im, -3.6863914024955916e-17 - 1.0981595540612889e-16im, 8.152524266830475e-17 + 1.0430422095906015e-17im, -2.340279079964355e-16 - 1.9934956557617644e-16im, -1.2779574767381416e-16 - 2.2387500508774194e-17im, 6.205712141534347e-18 + 7.25106688303849e-17im, -6.238328274614393e-18 - 3.254107922137993e-17im, 0.9999999999999994 + 1.9838393420767368e-17im  …  1.0000000000000002 - 2.7755575615628914e-17im, 0.0 + 5.204170427930421e-18im, 4.662069341687669e-18 - 6.965998958219366e-17im, 3.0357660829594124e-17 - 1.0972125985553305e-16im, 9.71445146547012e-17 + 1.682681771697503e-16im, 2.2551405187698492e-17 - 2.949029909160572e-17im, -8.326672684688674e-17 - 5.551115123125783e-17im, -2.2551405187698492e-17 + 0.0im, -1.3877787807814457e-17 - 3.903127820947816e-18im, 1.0 + 1.214306433183765e-17im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.2666916271667449 - 8.64866171311707e-18im, 0.6195142185620501 - 0.12159653347267643im, 0.08909365351457736 + 0.1486759506299938im, -1.4888926489870495e-5 - 0.003579058949151071im, -0.015122619084473087 - 0.0027639221857875687im, 0.0004605686692583218 + 0.0006478979569518893im, -2.6818704775755527e-13 + 1.004683541743659e-12im, -1.91042687571826e-12 - 1.4417540644422487e-12im, 0.61951421856205 + 0.12159653347267649im, -0.2666916271667502 - 2.728715561911604e-18im  …  0.16132256805248404 + 0.0im, 0.3740407531223581 - 0.5511592800958378im, -1.9104156191024346e-12 + 1.441754701736464e-12im, -2.8308486333056618e-12 + 4.1869724918056073e-13im, 0.0009327067211739575 + 0.0012588317089675858im, 0.004759108251099861 + 0.01455544773030865im, 0.010939445971500782 + 0.010294270599368343im, -0.15620595497866369 + 0.07368231398686512im, 0.3740407531223581 + 0.5511592800958378im, -0.16132256800655786 + 6.938893903907228e-18im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-2.3776060367912613 - 6.839248627694444e-17im, 0.04108333681734297 - 0.007964716614566183im, 0.04856324408013282 + 0.08025200635972932im, 0.021750895443393828 + 0.17559519375609903im, -0.007688183110628537 - 0.0022123352528942725im, 0.016127047719524685 - 0.0037289119543949404im, 3.472906738495838e-5 + 7.980395433348242e-5im, 7.136399586815424e-6 + 3.1742847820504443e-7im, 0.04108333681734295 + 0.00796471661456622im, -2.179473133142019 - 4.7323907061338206e-17im  …  2.174053493510243 + 5.551115123125783e-17im, 0.016509360086866737 - 0.01937877393121173im, 7.136399586776896e-6 - 3.17428478207888e-7im, 8.058227237808194e-5 - 3.288276862666896e-5im, -0.011220614780327626 - 0.012633769005603427im, 0.0023204434306361467 + 0.006347163065135386im, -0.18637004823991135 + 0.004712081071916237im, -0.05469275370228604 + 0.03937489647598129im, 0.01650936008686668 + 0.019378773931211714im, 2.3830256763601696 + 1.3877787807814457e-17im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8);;;], (⊞(ℂ^8) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^8)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999994 + 3.2202820414662736e-18im, -2.40952794409266e-17 + 3.649222716740275e-17im, -6.859380774282435e-17 - 1.5168739821422639e-18im, -3.335013710294403e-17 + 1.8472154729087577e-16im, -8.026977677946596e-17 + 7.969156717976266e-17im, 1.1750580168440233e-16 + 6.580921551844189e-17im, 1.8791863251044035e-17 - 6.442385369667312e-17im, 3.647922318123852e-18 - 4.277178281288766e-17im, -2.8102352466931516e-17 - 1.5348387629548716e-17im, 0.9999999999999998 + 9.353274763455213e-18im  …  0.9999999999999999 + 0.0im, 2.0816681711721685e-17 - 6.418476861114186e-17im, -1.940721888749053e-17 + 2.42861286636753e-17im, 5.2475385148298415e-17 + 6.071532165918825e-17im, -5.204170427930421e-17 + 1.3877787807814457e-16im, 5.204170427930421e-18 - 4.597017211338539e-17im, 1.1102230246251565e-16 - 2.2442984970449942e-17im, -4.5102810375396984e-17 - 1.3877787807814457e-17im, 4.163336342344337e-17 + 3.8163916471489756e-17im, 0.9999999999999994 - 1.3877787807814457e-17im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.3969814541927149 + 1.9711403924723457e-18im, -0.3427845732037283 + 0.43836536200541254im, 0.16349744738438357 - 0.0746750168959447im, -0.0002737040387040384 + 0.0002605889714741408im, -0.010735005281386004 + 0.017751661509222076im, 0.00021848219757204416 - 8.764002203135082e-6im, -2.109159099448991e-10 - 1.4362829413748736e-9im, 1.906404717372288e-9 + 1.516393242183619e-9im, -0.3427845732037283 - 0.43836536200541254im, -0.39698145419271086 - 6.78236194869089e-18im  …  0.06581463702337849 + 5.204170427930421e-18im, -0.3019203702526659 + 0.6097312948276249im, 1.9064046970825727e-9 - 1.516393255320686e-9im, 1.0980505174822824e-9 - 1.612451108046328e-9im, 0.002673562099512995 - 0.004798598741524622im, -0.014230128575415432 - 0.014061955459726983im, -0.005497070017839167 - 0.04621837400762879im, -0.15949016541477634 - 0.0685889807460159im, -0.3019203702526659 - 0.6097312948276249im, -0.06581463807764552 + 5.204170427930421e-18im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-3.3948409113519578 + 3.073496771601279e-16im, -0.020086044596221972 + 0.02568634086172418im, 0.1265330382870452 - 0.05805373420012741im, 0.00981909387870187 - 0.16572170725360919im, -0.008379733127358964 + 0.014246263775690509im, 0.006243104631921549 + 0.018880636374070992im, 4.093766068196133e-5 - 0.00011206295089189169im, 2.6390507216284334e-5 + 1.9150393417307908e-5im, -0.020086044596222007 - 0.025686340861724208im, -3.303425112739304 - 2.6374424971068304e-16im  …  0.6872712393749761 - 8.326672684688674e-17im, -0.00808332510825789 + 0.001990881148993635im, 2.6390507216373336e-5 - 1.9150393417423535e-5im, 2.2250455503374303e-5 + 0.00011721774742979446im, -0.007656240767291531 + 0.02212237380477096im, -0.007597341286537728 - 0.005372909635083939im, 0.05097374872104973 + 0.1898834918259177im, -0.07413444290381413 - 0.020025372108346734im, -0.008083325108257891 - 0.0019908811489937495im, 0.7983234108803803 - 1.3530843112619095e-16im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8);;;], (⊞(ℂ^8) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^8)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999996 + 6.037526721056975e-18im, 5.657405374976668e-17 - 2.673523976072199e-17im, 2.9694902324040897e-18 + 3.250995260405661e-17im, 5.0865792347870887e-17 - 6.178403895289779e-17im, 4.1454090911076997e-17 + 2.4086583777305094e-17im, 1.6150773109499874e-16 - 4.348689122226621e-17im, 7.974832762889246e-17 - 1.0331248920407577e-16im, -6.771800062314069e-17 - 5.623176925375647e-18im, 7.427608757122592e-17 + 4.6784321778508793e-17im, 0.9999999999999996 - 8.682749469400544e-18im  …  0.9999999999999996 + 0.0im, 2.7755575615628914e-17 + 1.3877787807814457e-16im, -5.876375774871434e-17 - 1.5395670849294163e-17im, 2.42861286636753e-17 + 2.168404344971009e-18im, -4.163336342344337e-17 + 7.632783294297951e-17im, 4.5102810375396984e-17 - 1.1796119636642288e-16im, 5.551115123125783e-17 + 1.6653345369377348e-16im, -6.245004513516506e-17 + 1.1102230246251565e-16im, 2.7755575615628914e-17 - 1.1102230246251565e-16im, 1.0000000000000004 + 0.0im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.2978322978342384 - 1.9678307539699364e-18im, -0.6113518804695066 + 0.06694025833208748im, -0.07128200347446201 - 0.16581912934463308im, -0.0003047213836298347 - 4.586187568540639e-5im, 0.01044305975997184 - 0.01847840226988672im, 0.0054984284441378746 + 0.0014226635990991774im, 5.539560275599325e-12 + 3.2916878345086278e-12im, 1.8615545061240087e-11 - 4.97675781219245e-13im, -0.6113518804695065 - 0.06694025833208748im, -0.29783229783424153 - 5.062615559811374e-19im  …  -0.3560186166165864 + 0.0im, -0.11331560515300865 - 0.5721420416539739im, 1.8615563300919402e-11 + 4.976730832995102e-13im, 1.7887217748646655e-11 + 4.845766149452757e-12im, -0.0058488695628842145 - 0.00879103307171226im, 0.0059458263132897045 - 0.018328151745850334im, -0.04998116602256865 + 0.04473683435980013im, -0.12450623137628157 + 0.11214231886788159im, -0.11331560515300867 + 0.5721420416539738im, 0.3560186166097278 + 1.3877787807814457e-17im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-4.444260296279691 + 2.3403717871159664e-16im, -0.014660564197035252 + 0.0016044774515792631im, -0.04207008680180082 - 0.09710812989313598im, 0.07388764645366558 - 0.16641662101231633im, 0.009005019491054244 - 0.005903725188480692im, 0.019703986552383746 - 0.013951476098507875im, -3.079394880889068e-5 + 0.0001010789827420644im, 5.6909597611522395e-5 + 1.0246586428360583e-5im, -0.014660564197035118 - 0.001604477451579676im, -4.383352411596497 + 2.1946764996318919e-16im  …  -0.5510609262267998 - 5.551115123125783e-17im, 0.0009979966430122382 + 0.01772641141984513im, 5.690959761168752e-5 - 1.0246586428569113e-5im, -0.00010327134585881581 + 2.2366671166187957e-5im, 0.013313880183873139 + 0.02281282211435745im, -8.424437122546424e-6 + 0.0038262450601937448im, 0.08379395658706104 - 0.182802289803765im, 0.06623040187310839 - 0.019644258567123485im, 0.0009979966430124394 - 0.017726411419845087im, -0.493450944782513 + 5.551115123125783e-17im], (ℂ^8 ⊗ (ℂ^1)') ← ℂ^8);;;], (⊞(ℂ^8) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^8)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0 + 0.0im, -3.599551212651875e-17 - 3.122502256758253e-17im, -2.5153490401663703e-17 - 6.505213034913027e-19im, 7.28583859910259e-17 - 2.0816681711721685e-17im, -6.158268339717665e-17 + 3.122502256758253e-17im, 0.9999999999999998 + 5.551115123125783e-17im, 7.28583859910259e-17 + 3.400058012914542e-16im, 2.7321894746634712e-17 + 1.8106176280507924e-17im, -5.854691731421724e-18 + 2.168404344971009e-18im, 7.632783294297951e-17 - 3.0531133177191805e-16im, 0.9999999999999997 + 5.551115123125783e-17im, -4.466912950640278e-17 - 1.734723475976807e-17im, 9.020562075079397e-17 + 2.7755575615628914e-17im, 3.447762908503904e-17 - 3.745918505937418e-17im, -2.7430314963883262e-17 + 2.0816681711721685e-17im, 0.9999999999999997 - 2.7755575615628914e-17im], (ℂ^4 ⊗ (ℂ^1)') ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.10350315371241428 - 1.3877787807814457e-17im, 0.2955035533027831 + 0.6083551245884804im, 0.13497485723512592 - 0.1150108820649396im, 0.0011892147057023616 - 0.0017721580506730437im, 0.2955035533027831 - 0.6083551245884804im, -0.10350315371241693 + 0.0im, 0.0009486167266005019 + 0.001911779819619114im, -0.11886938978848831 - 0.1315894496162626im, 0.13497485723512573 + 0.11501088206493928im, 0.0009486167266005262 - 0.0019117798196191154im, -0.08754380431724 + 4.7704895589362195e-18im, -0.6017607142710713 + 0.31361016492085675im, 0.0011892147057023694 + 0.0017721580506730255im, -0.11886938978848816 + 0.13158944961626237im, -0.6017607142710714 - 0.3136101649208567im, 0.08754380431724239 + 5.637851296924623e-18im], (ℂ^4 ⊗ (ℂ^1)') ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-5.503846440872673 + 0.0im, 0.001931290622051069 + 0.003977188790850281im, 0.027252879636676604 - 0.0226277296814643im, 0.06855094293446018 - 0.16942526008957268im, 0.0019312906220513171 - 0.003977188790850239im, -5.446065661903166 + 0.0im, -0.0776112870588162 - 0.29916343785461585im, 0.02331133643608473 + 0.02466836437031768im, 0.02725287963667661 + 0.022627729681464075im, -0.07761128705881554 + 0.29916343785461597im, -3.621161519291606 + 2.220446049250313e-16im, 0.0032490630840935485 - 0.0018570827132593504im, 0.06855094293446076 + 0.16942526008957115im, 0.02331133643608451 - 0.024668364370317546im, 0.0032490630840932757 + 0.0018570827132595863im, -3.5631892034293733 + 5.551115123125783e-16im], (ℂ^4 ⊗ (ℂ^1)') ← ℂ^4);;;], (⊞(ℂ^4) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^4)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0000000000000002 + 0.0im, -6.938893903907228e-18 + 2.0816681711721685e-17im, 2.0816681711721685e-17 - 4.163336342344337e-17im, 1.0000000000000002 + 2.7755575615628914e-17im], (ℂ^2 ⊗ (ℂ^1)') ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.00681011782269004 - 2.0816681711721685e-17im, 0.23386033966093212 - 0.6465705070715607im, 0.2338603396609322 + 0.6465705070715606im, -0.006810117822687575 - 3.469446951953614e-18im], (ℂ^2 ⊗ (ℂ^1)') ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-6.570319367984499 + 6.661338147750939e-16im, 0.00014878503371040797 - 0.00040883383852236im, 0.0001487850337100749 + 0.00040883383852236im, -6.48246925185002 - 4.440892098500626e-16im], (ℂ^2 ⊗ (ℂ^1)') ← ℂ^2);;;], (⊞(ℂ^2) ⊗ ((ℂ^1)' ⊞ (ℂ^1)' ⊞ (ℂ^1)')) ← ⊞(ℂ^2)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[6.8998701243686e-310 + 1.9131e-319im], (ℂ^1 ⊗ (ℂ^1)') ← ℂ^1);;;], (⊞(ℂ^1) ⊗ ⊞((ℂ^1)')) ← ⊞(ℂ^1))], BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}[BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.0 + 0.0im], (ℂ^1 ⊗ ℂ^1) ← ℂ^1);;;], (⊞(ℂ^1) ⊗ ⊞(ℂ^1)) ← ⊞(ℂ^1)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-6.5703212618964 + 0.0im, 0.00013076862092587654 - 7.614260499821252e-5im, 0.00013076862092588348 + 7.614260499813619e-5im, -6.4824673579380345 + 0.0im], (ℂ^2 ⊗ ℂ^1) ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.004735868964252687 - 3.209238430557093e-17im, -1.1710541612927374 + 0.7209518361219202im, -1.171054161292737 - 0.7209518361219202im, 0.0047358689642560126 - 3.469446951953614e-17im], (ℂ^2 ⊗ ℂ^1) ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999993 + 0.0im, 2.862293735361732e-17 + 2.6020852139652106e-18im, 1.1275702593849246e-17 + 3.5561831257524545e-17im, 1.0 - 6.938893903907228e-17im], (ℂ^2 ⊗ ℂ^1) ← ℂ^2);;;], (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^2)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-5.504054161072087 - 4.440892098500626e-16im, 0.0026863914980939096 + 0.000534632820854513im, -0.007161918147217245 + 0.03069911539884385im, 0.17401869052184638 - 0.05621127478846315im, 0.0026863914980936043 - 0.0005346328208544072im, -5.445857941703683 + 4.440892098500626e-16im, -0.07066512470264827 + 0.3008107234567169im, -0.03667286030146068 + 0.008462533144345695im, -0.0071619181472172486 - 0.030699115398844175im, -0.07066512470264753 - 0.3008107234567156im, -3.6208795553991022 + 4.440892098500626e-16im, -0.002017325937263099 - 0.005118804491193979im, 0.17401869052184732 + 0.05621127478846366im, -0.03667286030146065 - 0.00846253314434564im, -0.0020173259372628493 + 0.005118804491193896im, -3.5634711673227386 + 4.440892098500626e-16im], (ℂ^4 ⊗ ℂ^1) ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.12824076465340728 - 5.551115123125783e-17im, -1.338058175409508 - 0.2562800564327433im, 0.1436332343503716 - 0.32375599271837974im, 0.01765494548344979 + 0.00639792841129086im, -1.338058175409508 + 0.2562800564327433im, 0.12824076465340745 - 6.938893903907228e-18im, -0.0077879961551397 - 0.017087355086930604im, -0.3112456752021124 + 0.16904016830032703im, 0.1436332343503716 + 0.32375599271837946im, -0.0077879961551397285 + 0.017087355086930635im, 0.2416817846388732 + 2.7755575615628914e-17im, -0.9029445523149923 - 0.9994027677782001im, 0.017654945483449848 - 0.006397928411290861im, -0.3112456752021119 - 0.16904016830032687im, -0.9029445523149925 + 0.9994027677782003im, -0.24168178463887668 + 8.326672684688674e-17im], (ℂ^4 ⊗ ℂ^1) ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999994 - 5.551115123125783e-17im, 3.469446951953614e-18 + 9.974659986866641e-18im, -6.581107186987012e-17 + 1.214306433183765e-17im, 4.163336342344337e-17 + 6.938893903907228e-18im, 2.0816681711721685e-17 + 3.0357660829594124e-17im, 0.9999999999999993 - 5.551115123125783e-17im, -1.6653345369377348e-16 + 1.5265566588595902e-16im, -2.47198095326695e-17 - 1.3010426069826053e-17im, -5.648693318649478e-17 - 3.642919299551295e-17im, -1.6653345369377348e-16 - 1.942890293094024e-16im, 0.9999999999999993 - 5.551115123125783e-17im, 3.3393426912553537e-17 - 2.0816681711721685e-17im, -1.3877787807814457e-17 + 2.7755575615628914e-17im, -6.808789643208968e-17 - 1.214306433183765e-17im, 1.8648277366750676e-17 - 2.0816681711721685e-17im, 0.9999999999999996 + 0.0im], (ℂ^4 ⊗ ℂ^1) ← ℂ^4);;;], (⊞(ℂ^4) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^4)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-4.445648782675514 + 3.9946735394649257e-16im, 0.011236693440177959 - 0.002178427700109459im, 0.044256762133575024 + 0.07313543449327704im, 0.023377517300328717 + 0.1891518204604553im, -0.009563570037410995 - 0.0027519926151970244im, 0.023613261364204958 - 0.005554731936657266im, 4.787436979370387e-5 + 0.00011020020931761204im, 8.52871649162164e-6 + 3.793636816858005e-7im, 0.01123669344017781 + 0.0021784277001093083im, -4.3819639252007 + 4.781551109537209e-17im  …  -0.5553784581216262 + 1.5265566588595902e-16im, 0.004485808851915907 - 0.005265465916084108im, 8.528716491531304e-6 - 3.7936368161325777e-7im, 0.00011127310135532198 - 4.5324873637685864e-5im, -0.016376619878417875 - 0.018394637102440853im, 0.0028819474379925478 + 0.007883057899415041im, -0.19801663293685012 + 0.004744440877945094im, -0.04959303483718973 + 0.035703461017412494im, 0.004485808851916018 + 0.0052654659160840805im, -0.48913341014328987 + 1.6653345369377348e-16im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.46229049412303763 + 1.1177585016725724e-17im, -1.262024377157383 + 0.24764240507944935im, -0.18548527488842764 - 0.3096158304042702im, 2.6979261494315896e-5 + 0.006485381433703826im, 0.043203559426319135 + 0.007786418187490439im, -0.0011421918936098806 - 0.0016067610448533616im, -1.1102083519842486e-11 - 4.769864048053366e-12im, -1.714137281572309e-11 - 3.178325879326963e-12im, -1.2620243771573822 - 0.2476424050794493im, 0.46229049412303835 - 4.6158644528645494e-17im  …  -0.27780393529633196 + 0.0im, -0.7523082562564529 + 1.1066173916006772im, -1.7141341297766122e-11 + 3.178348209620374e-12im, 1.0895531059405134e-11 + 3.7390568072281916e-12im, -0.002309449849936574 - 0.0031169590491761526im, -0.013577514149564998 - 0.041613270197484106im, -0.019723362421056854 - 0.018560137854604662im, 0.32587996415533554 - 0.15289725222139683im, -0.752308256256453 - 1.1066173916006774im, 0.27780393528751346 + 2.7755575615628914e-17im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999994 - 5.4617129357086614e-17im, 2.0309359890008414e-17 + 6.5933451111452536e-18im, 1.9635964807060313e-17 + 2.4999407282142445e-17im, -1.973955614323999e-17 - 1.1284255441903445e-16im, -1.2159347639432695e-17 + 2.552180767596411e-17im, -2.58289382534131e-16 + 1.1818345674871596e-16im, -2.978427211471361e-17 + 1.0600191544527952e-16im, -9.810261464863386e-17 - 3.077479234544105e-17im, -2.139277828487203e-17 + 4.0105410946097284e-17im, 0.9999999999999996 - 3.350929568391234e-17im  …  1.0 - 5.551115123125783e-17im, 2.7755575615628914e-17 - 1.3877787807814457e-16im, -1.3357370765021415e-16 + 1.2996873542669984e-17im, 9.540979117872439e-18 - 1.4517467089580904e-16im, 1.249000902703301e-16 + 6.938893903907228e-18im, -7.45931094670027e-17 - 7.806255641895632e-17im, 1.6653345369377348e-16 + 5.551115123125783e-17im, 1.734723475976807e-17 - 7.632783294297951e-17im, 2.7755575615628914e-17 + 1.6653345369377348e-16im, 0.9999999999999996 + 0.0im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8);;;], (⊞(ℂ^8) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^8)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-3.396900136282725 - 1.0528624012086936e-16im, -0.018177173874008752 + 0.02324524780344607im, 0.1145191879695404 - 0.05254174395234335im, 0.010371215902234927 - 0.1745187660866399im, -0.007582092789611934 + 0.012890206903017128im, 0.0065446099547446955 + 0.01987504673424447im, 4.166147171410816e-5 - 0.00011272579078553784im, 2.365884061108233e-5 + 1.7167170889838345e-5im, -0.01817717387400859 - 0.023245247803446042im, -3.3013658878086303 + 1.535270855167758e-16im  …  0.6871395357653141 - 5.551115123125783e-17im, -0.0071786243576560035 + 0.0017680643768349935im, 2.365884061113861e-5 - 1.7167170889788655e-5im, 2.196927291012521e-5 + 0.00011815390473433841im, -0.007655328600886552 + 0.022493206035635087im, -0.006811544295881572 - 0.004817217106746388im, 0.05270982329037241 + 0.1923611108564865im, -0.06644892444184358 - 0.01794911478509892im, -0.007178624357655983 - 0.0017680643768350351im, 0.7984551360420905 + 2.7755575615628914e-17im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.7185089013481223 - 2.3347468483618623e-17im, 0.7164556126128485 - 0.9162288091198475im, -0.3270085362683356 + 0.14932050876763217im, 0.0004954336777088531 - 0.0004716939988688144im, 0.021492989787528557 - 0.035489905104227656im, -0.00039537113308213406 + 1.585956393446428e-5im, 8.706346370111008e-11 + 4.874224149058031e-10im, -7.221878654179095e-10 - 5.569218044246453e-10im, 0.7164556126128485 + 0.9162288091198475im, 0.7185089013481245 - 3.192241809241963e-17im  …  -0.11689709038183149 + 2.7755575615628914e-17im, 0.6058629929171203 - 1.2199606634048101im, -7.221879023619482e-10 + 5.56921825496659e-10im, -3.562869968672111e-10 + 5.743849606013041e-10im, -0.0047940684889801605 + 0.008604554533653441im, 0.02856304046665785 + 0.02843887850460875im, 0.009854389176640513 + 0.08285394350512777im, 0.3207250265526076 + 0.13930268502595466im, 0.6058629929171202 + 1.2199606634048104im, 0.11689709070046228 - 5.551115123125783e-17im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0000000000000002 + 6.991830083168891e-18im, 3.214542221116488e-17 - 5.908399047983421e-17im, -3.021268536612252e-17 + 3.595107866962096e-17im, 6.412281299500947e-17 - 1.6212526041583849e-16im, -2.454573513408677e-17 + 1.2866725190161472e-16im, -4.9834590165072004e-17 - 1.5539934067056598e-16im, -4.1976471570012563e-17 + 3.446036995937231e-17im, -2.869820776118698e-17 - 3.8843242906178386e-17im, 5.189341045273622e-17 + 3.8412533220610784e-17im, 0.9999999999999999 - 5.185779736828286e-17im  …  1.0000000000000002 + 0.0im, -2.7755575615628914e-17 + 9.020562075079397e-17im, -2.7592945289756088e-17 + 6.136584296267955e-17im, 5.4643789493269423e-17 + 3.2742905609062234e-17im, 1.3877787807814457e-16 - 1.8041124150158794e-16im, 6.938893903907228e-18 + 2.7755575615628914e-17im, -5.551115123125783e-17 - 1.6653345369377348e-16im, 3.426078865054194e-17 + 1.3877787807814457e-17im, -5.551115123125783e-17 - 1.1102230246251565e-16im, 1.0 + 2.7755575615628914e-17im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8);;;], (⊞(ℂ^8) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^8)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-2.37801794014371 - 6.059436210158901e-17im, -0.04061694598047145 + 0.00444518867770696im, -0.03502030173143497 - 0.08083548829961058im, 0.07293751859860491 - 0.16420556568216177im, 0.005482263877888468 - 0.0035941931464874123im, 0.013822045580112071 - 0.010171015303550114im, -2.2927606833828798e-5 + 7.58690020894644e-5im, 3.608081341791868e-5 + 6.496354082824612e-6im, -0.04061694598047143 - 0.004445188677707024im, -2.179061229789631 + 1.5779826016181834e-16im  …  2.1830692213236227 - 1.1102230246251565e-16im, 0.0027827808434534307 + 0.04942777510365785im, 3.60808134178452e-5 - 6.4963540827641265e-6im, -7.74238625638286e-5 + 1.6950702150634678e-5im, 0.0092142530782746 + 0.015878914329217335im, -5.145111525314827e-6 + 0.0023369089616760153im, 0.07704620358261485 - 0.17713594795019488im, 0.05531001777005293 - 0.016405220050568867im, 0.002782780843453389 - 0.04942777510365781im, 2.3740099486028203 + 0.0im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.5207815684089834 - 2.43652927537769e-18im, 1.2603861638171008 - 0.13800473861326226im, 0.13690406726028664 + 0.3185547349893393im, 0.0005102871980751704 + 7.680041279573968e-5im, -0.014425186054071759 + 0.026299154976168214im, -0.006716228897156274 - 0.0017377573355434027im, -3.0495667649288137e-13 + 6.323244438282329e-15im, -5.838436808152962e-13 + 4.2709040170804325e-14im, 1.260386163817101 + 0.13800473861326226im, 0.5207815684089825 - 8.095317323210366e-19im  …  0.626542032137591 - 2.7755575615628914e-17im, 0.230092209486163 + 1.1972195658777947im, -5.83854579266907e-13 - 4.2674197509029455e-14im, -6.778672675261666e-13 - 2.2346447609011832e-13im, 0.007167251036665176 + 0.010772601474208311im, -0.008564488556589735 + 0.026591167370445066im, 0.08396881934502982 - 0.07515829354824385im, 0.23989118065083442 - 0.2235459658197913im, 0.230092209486163 - 1.1972195658777947im, -0.6265420321392837 - 1.3877787807814457e-17im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999999 - 3.9853866516294405e-17im, 3.7293709549943e-18 + 2.5095981413721406e-17im, -8.731244566891554e-18 + 3.7987200419378346e-17im, 1.2610372384170103e-16 - 1.4429364615919763e-16im, -4.559643041199208e-17 + 3.271010772700051e-17im, 7.25733275324836e-17 + 1.2539358248407886e-16im, -2.5616884460932484e-17 + 4.918653093911486e-17im, -1.7298302475442547e-17 - 5.25120055083026e-17im, 1.6202448056114438e-17 - 3.3557505546816516e-17im, 1.0000000000000002 - 1.3526116533261408e-17im  …  1.0000000000000013 - 5.551115123125783e-17im, -6.938893903907228e-17 + 3.469446951953614e-18im, -1.8106176280507924e-17 + 4.586175189613684e-17im, -1.0928757898653885e-16 - 1.0039712117215771e-16im, -4.5102810375396984e-17 - 2.1510571102112408e-16im, 1.734723475976807e-18 + 1.5265566588595902e-16im, -2.7755575615628914e-16 + 1.249000902703301e-16im, -2.0816681711721685e-17 - 4.163336342344337e-17im, -6.938893903907228e-17 + 3.8163916471489756e-17im, 1.0000000000000004 + 0.0im], (ℂ^8 ⊗ ℂ^1) ← ℂ^8);;;], (⊞(ℂ^8) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^8)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-1.4046035551305536 + 5.551115123125783e-17im, 0.01121036137093855 + 0.023085973222826635im, 0.017190192754933283 - 0.01427280492993639im, 0.05624436378603348 - 0.13906112670806714im, 0.011210361370938567 - 0.023085973222826652im, -0.9686314206324347 + 5.551115123125783e-17im, -0.06354912473435931 - 0.24500469902269378im, 0.014704000900102529 + 0.015559968125630458im, 0.017190192754933255 + 0.01427280492993637im, -0.0635491247343592 + 0.24500469902269328im, 0.9682020425075444 - 2.7755575615628914e-17im, 0.018846951163607673 - 0.010772443100764022im, 0.05624436378603326 + 0.13906112670806708im, 0.014704000900102515 - 0.015559968125630428im, 0.01884695116360766 + 0.010772443100764017im, 1.4050329332554452 + 0.0im], (ℂ^4 ⊗ ℂ^1) ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.1617028938007031 + 6.938893903907228e-18im, -0.6001084848725136 - 1.235449102792022im, -0.22498309737415023 + 0.19173561269434602im, -0.0015316612679604144 + 0.0022824691237549287im, -0.6001084848725133 + 1.235449102792022im, 0.1617028938006999 + 0.0im, -0.0012217806349641182 - 0.002462296412045692im, 0.1981338307320366 + 0.21936937889959163im, -0.22498309737415 - 0.1917356126943459im, -0.0012217806349641216 + 0.002462296412045692im, 0.1366786263360216 + 3.469446951953614e-18im, 1.220329733445776 - 0.6361814205399109im, -0.0015316612679604144 - 0.0022824691237549356im, 0.19813383073203653 - 0.21936937889959168im, 1.220329733445776 + 0.6361814205399108im, -0.13667862633601827 + 6.938893903907228e-18im], (ℂ^4 ⊗ ℂ^1) ← ℂ^4) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[0.9999999999999999 + 0.0im, -7.806255641895632e-18 + 1.734723475976807e-17im, -5.204170427930421e-18 - 8.673617379884035e-19im, -5.551115123125783e-17 - 1.942890293094024e-16im, -1.0408340855860843e-17 - 2.0816681711721685e-17im, 1.0000000000000004 + 0.0im, 0.0 + 2.7755575615628914e-16im, 1.8865117801247777e-17 - 1.4094628242311558e-18im, -8.673617379884035e-18 + 2.6020852139652106e-18im, -1.3877787807814457e-17 - 3.3306690738754696e-16im, 1.000000000000001 + 0.0im, -7.806255641895632e-18 - 6.5052130349130266e-18im, 0.0 + 2.0816681711721685e-16im, 1.9949319973733282e-17 + 3.3610267347050637e-18im, -6.071532165918825e-18 + 3.469446951953614e-18im, 1.0000000000000007 + 0.0im], (ℂ^4 ⊗ ℂ^1) ← ℂ^4);;;], (⊞(ℂ^4) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^4)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.4999915654132384 + 0.0im, 0.000993195070784805 - 0.002729116921420289im, 0.000993195070784805 + 0.002729116921420289im, 0.49999156541323864 + 0.0im], (ℂ^2 ⊗ ℂ^1) ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[-0.00821436926931063 + 2.168404344971009e-19im, -0.48100686511817936 + 1.3298740240514102im, -0.4810068651181794 - 1.32987402405141im, 0.008214369269310632 + 0.0im], (ℂ^2 ⊗ ℂ^1) ← ℂ^2) TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0000000000000002 + 0.0im, 4.336808689942018e-19 - 4.336808689942018e-19im, 4.336808689942018e-19 + 4.336808689942018e-19im, 1.0000000000000007 + 0.0im], (ℂ^2 ⊗ ℂ^1) ← ℂ^2);;;], (⊞(ℂ^2) ⊗ (ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1)) ← ⊞(ℂ^2)), BlockTensorKit.BlockTensorMap{TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}, ComplexF64, TensorKit.ComplexSpace, 2, 1, 3}(TensorKit.TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}[TensorMap{ComplexF64, TensorKit.ComplexSpace, 2, 1, Vector{ComplexF64}}(ComplexF64[1.0 + 0.0im], (ℂ^1 ⊗ ℂ^1) ← ℂ^1);;;], (⊞(ℂ^1) ⊗ ⊞(ℂ^1)) ← ⊞(ℂ^1))]), 5.108673279231418e-12)

1. Entanglement entropy at a single cut ​

entropy returns the von Neumann entanglement entropy across the cut to the right of a given site. For a FiniteMPS the site is a required argument:

julia
entropy(ψ, L ÷ 2)   # entropy across the central cut
0.6885976457856061

2. Entropy profile across every cut ​

Collecting entropy(ψ, i) over the valid range of sites gives the full entropy profile of the chain:

julia
[entropy(ψ, i) for i in 1:L]
8-element Vector{Float64}:
  0.5687362834103672
  0.6619622060572383
  0.6843192424818717
  0.6885976457856061
  0.6843192424818836
  0.6619622060572788
  0.5687362834104189
 -4.440892098500627e-16

Warning

For FiniteMPS the cut site is required and must lie in 1:length(ψ). site = 0 — a valid default for InfiniteMPS and WindowMPS (see recipe 5) — throws a BoundsError for FiniteMPS.

3. The entanglement spectrum ​

entanglement_spectrum returns the singular values of the gauge tensor to the right of a site, packaged as a sector-resolved vector:

julia
spectrum = entanglement_spectrum(ψ, L ÷ 2)
8-element TensorKit.SectorVector{Float64, TensorKitSectors.Trivial, Vector{Float64}}:
 0.747993377176481
 0.6634940095407499
 0.012553077940045912
 0.011134980961941746
 0.00014854190117707638
 0.00013176140934784798
 2.4928804504691113e-6
 2.2112645586263168e-6

The entropy can equivalently be computed directly from this spectrum with entropy:

julia
entropy(spectrum)
0.6885976457856061
julia
entropy(ψ, L ÷ 2) ≈ entropy(spectrum)
true

Both routes agree, since entropy(ψ, site) computes the entropy from exactly this spectrum internally.

4. Sector-resolved spectrum ​

Because the returned spectrum is indexed by symmetry sector, you can inspect the singular values sector by sector. Use keys to list the sectors present at a cut, and index the spectrum with a sector to obtain its singular values:

julia
collect(keys(spectrum))
1-element Vector{TensorKitSectors.Trivial}:
 Trivial()
julia
spectrum[only(keys(spectrum))]
8-element view(::Vector{Float64}, 1:8) with eltype Float64:
 0.747993377176481
 0.6634940095407499
 0.012553077940045912
 0.011134980961941746
 0.00014854190117707638
 0.00013176140934784798
 2.4928804504691113e-6
 2.2112645586263168e-6

For the plain (no explicit symmetry) FiniteMPS built above there is a single sector, Trivial(), so all singular values live in one block. pairs(spectrum) iterates sector => values pairs and is the natural entry point for a symmetric state where multiple sectors are populated at a cut:

julia
collect(pairs(spectrum))
1-element Vector{Pair{TensorKitSectors.Trivial, SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}}}:
 Trivial() => [0.747993377176481, 0.6634940095407499, 0.012553077940045912, 0.011134980961941746, 0.00014854190117707638, 0.00013176140934784798, 2.4928804504691113e-6, 2.2112645586263168e-6]

5. Entanglement of an infinite MPS ​

For InfiniteMPS, the cut site defaults to 0, and entropy without a site argument returns one entropy per site in the unit cell:

julia
ψ∞ = InfiniteMPS(ℂ^2, ℂ^8)
entropy(ψ∞)
1-element Vector{Float64}:
 0.00045748508039131604
julia
entanglement_spectrum(ψ∞)   # site defaults to 0
8-element TensorKit.SectorVector{Float64, TensorKitSectors.Trivial, Vector{Float64}}:
 0.9999795031169677
 0.006370177056143807
 0.0006333569623596394
 0.00011392278780630928
 7.744962455067506e-6
 3.143608573845967e-6
 9.228542555243811e-7
 2.3243321878357342e-7

Note

ψ∞ here is a random InfiniteMPS, not a converged ground state, so the values above illustrate the interface rather than any physical entanglement profile. For a physically meaningful result, compute the entropy of a state obtained from find_groundstate (for example via VUMPS).

Note

WindowMPS also supports entropy(ψ, site) with a required site argument, mirroring the FiniteMPS form.

Plotting the spectrum ​

MPSKit defines an entanglementplot recipe via RecipesBase, but does not depend on Plots.jl itself. To use it, add using Plots (or another Plots-backed package) in your own environment:

julia
using Plots
entanglementplot(ψ; site = L ÷ 2)

Note

entanglementplot is a plotting recipe: it only becomes available once Plots (or a compatible plotting package) is loaded. This block is not executed on this page to keep the docs build free of the Plots.jl dependency.