Sweeping through the MPS

mutable struct SweepData
    sweepcount::Int
    maxchi::Vector{Int}
    energy::Vector{Float64}
    entropy::Vector{Float64}
    maxtruncerr::Vector{Float64}
    lasteigs::Vector{Vector{Float64}}
end

Holds historical data after each (full)sweep. Requires for convergence check etc.

• sweepcount::Int: Number of fullsweeps performed.
• maxchi::Vector{Int}: Maximum MPS bond/link dimensions after every sweep.
• energy::Vector{Float64}: Energies after every sweep.
• entropy::Vector{Float64}: Mid-chain entropies after every sweep.
• maxtrucerr::Vector{Float64}: Maximum truncation error after every sweep.
• lasteigs::Vector{Vector{Float64}}: Spectrum of eigenvalues at each bond after previous halfsweep.

Default constructor:

• SweepData(): Initialize an empty SweepData object.

Base.copy(swdata::SweepData)

Shallow copy of SweepData.

function fullsweep!(sysenv::StateEnvs, solver, nsite::Int, swdata::SweepData;
                    kwargs...)

Perform a fullsweep (left-to-right and right-to-left) by solver.

Arguments:

• sysenv::StateEnvs.
• solver: Solver for update. Available ones: eig_solver and exp_solver.
• nsite::Int of the environment. Either 1 or 2 for one-site or two-site update respectively.
• swdata::SweepData.

Named arguments and their default values:

• time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP.
• normalize::Bool = true: Whether to normalize after update.
• maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
• mindim::Int = 1: Minimum bond dimension after SVD truncation.
• cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
• svd_alg::String = "divide_and_conquer".
• noise::Float64 = 0.0.
• reverse_step::Bool = false if time_step = nothing, true otherwise.
• outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

• ishermitian::Bool = true.
• solver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.
• solver_krylovdim::Int = 5 if eig_solver, 30 if exp_solver.
• solver_maxiter::Int = 2 if eig_solver, 100 if exp_solver.
• solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
• solver_eager::Bool = false if eig_solver, true if exp_solver.
• solver_check_convergence::Bool = false if eig_solver, true if exp_solver.

Return values:

• ::Float64: Change in Energy ΔE
• ::Float64: Change in Entropy ΔS

swdata::SweepData gets updated.

function dynamic_fullsweep!(sysenv::StateEnvs, solver, swdata::SweepData;
                            kwargs...)

Perform a dynamic fullsweep (left-to-right and right-to-left) by solver. The very first sweep, as dictated by swdata.sweepcount=0, Global Subspace Expansion (see below) is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep. At each bond, if the lowest eigenvalue is below eigthreshold or the bond dimension at that bond has reached maxdim at a particular halfsweep, performs single-site update across that bond in the subsequent halfsweep, otherwise performs two-site update.

Arguments:

• sysenv::StateEnvs.
• solver: Solver for update. Available ones: eig_solver and exp_solver.
• swdata::SweepData.

Named arguments and their default values:

• time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP.
• normalize::Bool = true: Whether to normalize after update.
• maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
• mindim::Int = 1: Minimum bond dimension after SVD truncation.
• cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
• svd_alg::String = "divide_and_conquer".
• noise::Float64 = 0.0.
• reverse_step::Bool = false if time_step = nothing, true otherwise.
• outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.
• eigthreshold::Float64 = 1E-12.
• extendat::Union{Nothing, Int} = nothing: If specified, at every extendatth sweep, Global Subspace Expansion is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

• ishermitian::Bool = true.
• solver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.
• solver_krylovdim::Int = 3 if eig_solver, 30 if exp_solver.
• solver_maxiter::Int = 1 if eig_solver, 100 if exp_solver.
• solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
• solver_eager::Bool = false if eig_solver, true if exp_solver.
• solver_check_convergence::Bool = false if eig_solver, true if exp_solver.

Arguments for Global Subspace Expansion and their default values:

• extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
• extension_applyH_cutoff::Float64 = 0.0: Cutoff for the application of the MPO to the MPS.
• extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension for the application of the MPO to the MPS.
• extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.

Return values:

• ::Float64: Change in Energy ΔE
• ::Float64: Change in Entropy ΔS

swdata::SweepData gets updated.

function krylov_extend!(psi::MPS, H::MPO; kwargs...)

Performs Global Subspace Expansion.

Named arguments and their default values:

• extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
• extension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.
• extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.
• extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.

function krylov_extend!(sysenv::StateEnvs{ProjMPO}; kwargs...)

Performs Global Subspace Expansion. The StateEnvs must be created by a single MPO.

Named arguments and their default values:

• extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
• extension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.
• extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.
• extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.