MPSKit.jl

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How-to guides ​

These pages are task recipes: short, runnable answers to "how do I do X?". They assume you already know the basics — if you are new to MPSKit, start with Your first ground state instead. Each recipe below stands on its own, so feel free to jump straight to the one you need.

States and operators ​

Constructing states — building FiniteMPS, InfiniteMPS, WindowMPS, and MultilineMPS objects.

  • A finite MPS — random states, initializers and element types, per-site spaces, product states, and wrapping your own site tensors.

  • An infinite MPS — single- and multi-site unit cells, from spaces or from tensors.

  • A window MPS — a mutable finite region embedded in infinite environments.

  • A multiline MPS — stacking InfiniteMPS rows for boundary-MPS methods.

  • States with symmetries — building MPS with Rep[G] graded spaces.

Building Hamiltonians — assembling MPO Hamiltonians from local operators.

  • Finite Hamiltonian from local terms — FiniteMPOHamiltonian from inds => operator pairs.

  • Infinite (translation-invariant) Hamiltonian — InfiniteMPOHamiltonian on a unit cell.

  • Converting between boundary conditions — open vs. periodic finite chains from an infinite Hamiltonian.

  • A window Hamiltonian — carving a finite interval out of an infinite Hamiltonian with WindowMPOHamiltonian.

Finding ground states ​

Ground-state algorithms — configuring find_groundstate.

  • Get a ground state with defaults — letting find_groundstate pick an algorithm for you.

  • Configure finite-system DMRG — explicit DMRG/DMRG2, and chaining them with &.

  • Configure infinite-system algorithms — VUMPS, IDMRG, and IDMRG2.

  • Refine convergence with GradientGrassmann — Riemannian gradient descent after a cheaper warm-up.

  • Control output and tolerances — verbosity levels and reusing envs between calls.

Controlling bond dimension — inspecting, growing, and shrinking bond dimension.

  • Inspecting the current bond dimension — left_virtualspace/right_virtualspace and dim.

  • Growing bond dimension — RandExpand (no Hamiltonian needed) and OptimalExpand.

  • Reducing bond dimension — SvdCut and the in-place changebonds!.

  • Truncation schemes — truncrank, trunctol, notrunc, truncspace, and combining them with &.

  • Growing during finite MPS optimization — DMRG2 and the trscheme keyword of find_groundstate.

  • Growing during infinite MPS optimization — IDMRG2 and VUMPSSvdCut.

  • Chaining algorithms — composing bond-change and ground-state algorithms with &.

Dynamics ​

Time evolution — real- and imaginary-time evolution of an MPS.

  • Evolve a state through one time step — timestep with TDVP.

  • Evolve over a time span — time_evolve across a vector of time points.

  • Grow the bond dimension while evolving — TDVP2 with a mandatory trscheme.

  • Evolve an infinite state — single-site TDVP on an InfiniteMPS.

  • Imaginary-time evolution — imaginary_evolution = true to cool towards the ground state.

  • Build a time-evolution MPO — make_time_mpo (WII, TaylorCluster, WI) plus approximate.

Measurements ​

Computing observables — extracting physical quantities from an MPS.

  • Local (one-site) expectation value — expectation_value(ψ, i => O).

  • Multi-site (contiguous) expectation value — tensor-product operators on an index tuple.

  • Energy (full-MPO expectation value) — expectation_value(ψ, H) for a Hamiltonian MPO.

  • Two-point correlators — correlator, including a full correlation profile over a range.

  • Energy variance as a convergence check — variance as a diagnostic after a ground-state search.

Entanglement entropy and spectrum — reading off entanglement from the gauge tensors.

  • Entanglement entropy at a single cut — entropy(ψ, site).

  • Entropy profile across every cut — collecting entropy over all sites.

  • The entanglement spectrum — entanglement_spectrum as a sector-resolved vector.

  • Sector-resolved spectrum — indexing the spectrum by symmetry sector with keys/pairs.

  • Entanglement of an infinite MPS — entropy/entanglement_spectrum per unit-cell site.

  • Plotting the spectrum — the entanglementplot recipe (requires Plots.jl).

Excitations ​

Excited states — computing energy eigenstates beyond the ground state.

  • Get a single excitation gap on an infinite chain — QuasiparticleAnsatz at a fixed momentum.

  • Scan the dispersion relation — passing a range of momenta in one call.

  • Target a symmetry sector — a charged quasiparticle via the sector keyword.

  • Excited states on a finite chain — QuasiparticleAnsatz, FiniteExcited, and the Chepiga ansätze.

  • Check excitation quality — variance on a quasiparticle state.

  • Domain-wall excitations — quasiparticles interpolating between two distinct ground states.

Missing a recipe? ​

If the task you're after isn't listed here, please open an issue at QuantumKitHub/MPSKit.jl describing what you're trying to do. Concrete task descriptions make the best new recipes.