Performing DMRG

mutable struct DMRGParams
    maxdim::Vector{Int}
    nsweeps::Vector{Int}
    cutoff::Vector{Float64}
    noise::Vector{Float64}
    noisedecay::Vector{Float64}
    disable_noise_after::Vector{Int}
end

Holds parameters to control DMRG sweeps.

• maxdim::Vector{Int}: Maximum allowed MPS bond/link dimensions at each stages of DMRG.
• nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of DMRG.
• cutoff::Vector{Float64}: Cutoff for SVD truncation at each stages of DMRG.
• noise::Vector{Float64}: Noise level at each stages of DMRG.
• noisedecay::Vector{Float64}: Decay of noise level at each states of DMRG. Noise is divided by noisedecay after each sweep.
• disable_noise_after::Vector{Int}: Switch of noise after this many sweeps at each

states of DMRG.

All these Vectors must have same dimension.

function DMRGParams(;maxdim::Vector{Int}, nsweeps::Vector{Int}, 
                    cutoff::Union{Vector{Float64}, Float64, Int} = _Float64_Threshold,
                    noise::Union{Vector{Float64}, Float64, Int} = 0.0,
                    noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0,
                    disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))

Constructor for DMRGParams. Takes only named arguments.

• maxdim::Vector{Int}: Maximum allowed MPS bond/link dimensions at each stages of DMRG.
• nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of DMRG.
• cutoff::Union{Int, Float64, Vector{Float64}} = Float64_threshold(): Cutoff for SVD truncation at each stages of DMRG. If Float64, cutoff remains same throughout the DMRG simulation.
• noise::Union{Float64, Int, Vector{Float64}} = 0.0: Noise level at each stages of DMRG. If Float64 or Int, initial noise remains same throughout the DMRG simulation.
• noisedecay::Union{Float64, Int, Vector{Float64}} = 1.0: Decay of noise level at each states of DMRG. Noise is divided by noisedecay after each sweep. If Float64 or Int, noisedecay remains same throughout the DMRG simulation.
• disable_noise_after::Union{Int, Vector{Int}} = typemax(Int): Switch of noise after this many sweeps at each states of DMRG. If Int, disable_noise_after remains same throughout the DMRG simulation.

Base.copy(params::DMRGParams)

Shallow copy DMRGParams.

function dmrg!(sysenv::StateEnvs, params::DMRGParams, nsite::Int; kwargs...)

Performs DMRG.

Arguments:

• sysenv::StateEnvs.
• params::DMRGParams.
• nsite::Int of the environment. Either 1 or 2 for one-site or two-site update respectively.

Named arguments and their default values:

• normalize::Bool = true: Whether to normalize after update.
• svd_alg::String = "divide_and_conquer".
• weight::Float64 = -1.0: Weight for the excited state DMRG. Must be set to greater than 0 for the excited state DMRG.
• outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

• energyErrGoal: DMRG (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.
• entropyErrGoal: DMRG (at a particluar stage) stops when mid-chain entropy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.

When both energyErrGoal and entropyErrGoal are given, both conditions must be satisfied to trigger this early stopping.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

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

Return values:

• SweepData

function dmrg2(psi0::MPS, H::MPO, params::DMRGParams; kwargs...)
function dmrg2(psi0::MPS, H::CouplingModel, params::DMRGParams; kwargs...)
function dmrg2(psi0::MPS, Hs::Vector{MPO}, params::DMRGParams; kwargs...)
function dmrg2(psi0::MPS, H::MPO, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
function dmrg2(psi0::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
function dmrg2(psi0::MPS, H::CouplingModel, Ms::Vector{MPS}, params::DMRGParams; kwargs...)

Performs two-site DMRG.

Arguments:

• psi0::MPS: Initial MPS.
• H::MPO, H::CouplingModel, Hs::Vector{MPO}, Ms::Vector{MPS}.
• params::DMRGParams.

Named arguments and their default values:

• normalize::Bool = true: Whether to normalize after update.
• svd_alg::String = "divide_and_conquer".
• weight::Float64 = -1.0: Weight for the excited state DMRG. Must be set to greater than 0 for the excited state DMRG.
• outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

• energyErrGoal: DMRG (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.
• entropyErrGoal: DMRG (at a particluar stage) stops when mid-chain entropy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.

When both energyErrGoal and entropyErrGoal are given, both conditions must be satisfied to trigger this early stopping.

Named arguments for eig_solver and their default values:

See the documentation of KrylovKit.jl.

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

Return values:

• ::Float64: Energy.
• ::MPS: The state psi.

function dmrg1(psi0::MPS, H::MPO, params::DMRGParams; kwargs...)
function dmrg1(psi0::MPS, H::CouplingModel, params::DMRGParams; kwargs...)
function dmrg1(psi0::MPS, Hs::Vector{MPO}, params::DMRGParams; kwargs...)
function dmrg1(psi0::MPS, H::MPO, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
function dmrg1(psi0::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
function dmrg1(psi0::MPS, H::CouplingModel, Ms::Vector{MPS}, params::DMRGParams; kwargs...)

Performs single-site DMRG. All other details are same as in dmrg2.