MPSKit.jl

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Ground-state algorithms ​

Reference for the ground-state search interface and its algorithms. For a task-oriented walkthrough see the how-to guides; the full, canonical docstrings for the whole package live in the Library index.

Interface ​

MPSKit.find_groundstate Function
julia
find_groundstate(ψ₀, H, [environments]; kwargs...) -> (ψ, environments, ϵ)
find_groundstate(ψ₀, H, algorithm, environments) -> (ψ, environments, ϵ)

Compute the ground state for Hamiltonian H with initial guess ψ. If not specified, an optimization algorithm will be attempted based on the supplied keywords.

Arguments

  • ψ₀::AbstractMPS: initial guess

  • H::AbstractMPO: operator for which to find the ground state

  • [environments]: MPS environment manager

  • algorithm: optimization algorithm

Keyword Arguments

  • tol::Float64: tolerance for convergence criterium

  • maxiter::Int: maximum amount of iterations

  • verbosity::Int: display progress information

Returns

  • ψ::AbstractMPS: converged ground state

  • environments: environments corresponding to the converged state

  • ϵ::Float64: final convergence error upon terminating the algorithm

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Algorithms ​

MPSKit.DMRG Type
julia
struct DMRG{A, F, E, G} <: MPSKit.Algorithm

Density Matrix Renormalization Group algorithm for finding the dominant eigenvector.

Each site update is, in order: (1) an optional bond expansion (alg_expand), (2) a single-site eigensolve, and (3) a gauge step (alg_gauge). With the defaults (alg_expand = nothing and a non-truncating QR alg_gauge) this is textbook single-site DMRG, which cannot change the bond dimension. Setting alg_expand to a bond-expansion algorithm (e.g. OptimalExpand, RandExpand, SketchedExpand) enriches the bond with directions orthogonal to the current state ahead of each eigensolve, recovering Controlled Bond Expansion (CBE) DMRG; a truncating alg_gauge is then desirable to cut the enlarged bond back down.

The gauge algorithm is selected in the keyword constructor from the trscheme argument: when it is notrunc() the gauge is a QR decomposition (alg_orth, Householder by default), otherwise it is a truncated SVD (alg_svd with the given trscheme).

Fields

  • tol::Float64: tolerance for convergence criterium

  • maxiter::Int64: maximal amount of iterations

  • verbosity::Int64: setting for how much information is displayed

  • alg_eigsolve::Any: algorithm used for the eigenvalue solvers

  • finalize::Any: callback function applied after each iteration, of signature finalize(iter, ψ, H, envs) -> ψ, envs

  • alg_expand::Any: algorithm used to expand the bond ahead of each local update, or nothing for none

  • alg_gauge::Any: factorization used for the post-update gauge: a QR algorithm (no truncation) or a truncated SVD

See also

Used as the algorithm argument of find_groundstate and approximate.

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MPSKit.DMRG2 Type
julia
struct DMRG2{A, S, F} <: MPSKit.Algorithm

Two-site DMRG algorithm for finding the dominant eigenvector.

Fields

  • tol::Float64: tolerance for convergence criterium

  • maxiter::Int64: maximal amount of iterations

  • verbosity::Int64: setting for how much information is displayed

  • alg_eigsolve::Any: algorithm used for the eigenvalue solvers

  • alg_svd::Any: algorithm used for the singular value decomposition

  • trscheme::MatrixAlgebraKit.TruncationStrategy: algorithm used for truncation of the two-site update

  • finalize::Any: callback function applied after each iteration, of signature finalize(iter, ψ, H, envs) -> ψ, envs

See also

Used as the algorithm argument of find_groundstate and approximate.

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MPSKit.VUMPS Type
julia
struct VUMPS{F} <: MPSKit.Algorithm

Variational optimization algorithm for uniform matrix product states, based on the combination of DMRG with matrix product state tangent space concepts.

Fields

  • tol::Float64: tolerance for convergence criterium

  • maxiter::Int64: maximal amount of iterations

  • verbosity::Int64: setting for how much information is displayed

  • alg_gauge::Any: algorithm used for gauging the InfiniteMPS

  • alg_eigsolve::Any: algorithm used for the eigenvalue solvers

  • alg_environments::Any: algorithm used for the MPS environments

  • finalize::Any: callback function applied after each iteration, of signature finalize(iter, ψ, H, envs) -> ψ, envs

See also

Used as the algorithm argument of find_groundstate and leading_boundary.

References

source
MPSKit.IDMRG Type
julia
struct IDMRG{A} <: MPSKit.Algorithm

Single site infinite DMRG algorithm for finding the dominant eigenvector.

Fields

  • tol::Float64: tolerance for convergence criterium

  • maxiter::Int64: maximal amount of iterations

  • verbosity::Int64: setting for how much information is displayed

  • alg_gauge::Any: algorithm used for gauging the MPS

  • alg_eigsolve::Any: algorithm used for the eigenvalue solvers

See also

Used as the algorithm argument of find_groundstate, leading_boundary, and approximate.

source
MPSKit.IDMRG2 Type
julia
struct IDMRG2{A, S} <: MPSKit.Algorithm

Two-site infinite DMRG algorithm for finding the dominant eigenvector.

Fields

  • tol::Float64: tolerance for convergence criterium

  • maxiter::Int64: maximal amount of iterations

  • verbosity::Int64: setting for how much information is displayed

  • alg_gauge::Any: algorithm used for gauging the MPS

  • alg_eigsolve::Any: algorithm used for the eigenvalue solvers

  • alg_svd::Any: algorithm used for the singular value decomposition

  • trscheme::MatrixAlgebraKit.TruncationStrategy: algorithm used for truncation of the two-site update

See also

Used as the algorithm argument of find_groundstate, leading_boundary, and approximate.

source
MPSKit.GradientGrassmann Type
julia
struct GradientGrassmann{O<:OptimKit.OptimizationAlgorithm, F} <: MPSKit.Algorithm

Variational gradient-based optimization algorithm that keeps the MPS in left-canonical form, as points on a Grassmann manifold. The optimization is then a Riemannian gradient descent with a preconditioner to induce the metric from the Hilbert space inner product.

Constructors

julia
GradientGrassmann(; kwargs...)

Keyword Arguments

  • method = ConjugateGradient: instance of optimization algorithm, or type of optimization algorithm to construct

  • finalize!: finalizer algorithm

  • tol = Defaults.tol: tolerance for convergence criterium

  • maxiter = Defaults.maxiter: maximum amount of iterations

  • verbosity = Defaults.verbosity - 1: level of information display

Fields

  • method::OptimKit.OptimizationAlgorithm: optimization algorithm

  • finalize!::Any: callback function applied after each iteration, of signature finalize!(x, f, g, numiter) -> x, f, g

See also

Used as the algorithm argument of find_groundstate and leading_boundary.

References

source