Optimizing TTN

mutable struct OptimizeParamsTTN
    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 the optimzation sweeps of the TTN.

• maxdim::Vector{Int}: Maximum allowed TTN bond/link dimensions at each stages of optimization.
• nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of optimization.
• cutoff::Vector{Float64}: Cutoff for SVD truncation at each stages of optimization.
• noise::Vector{Float64}: Noise level at each stages of optimization.
• noisedecay::Vector{Float64}: Decay of noise level at each states of optimization.

Noise is divided by noisedecay after each sweep.

• disable_noise_after::Vector{Int}: Switch of noise after this many sweeps at each

states of optimization.

All these Vectors must have same dimension.

function OptimizeParamsTTN(;maxdim::Vector{Int}, nsweeps::Vector{Int}, 
                           cutoff::Union{Vector{Float64}, Float64} = 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 OptimizeParamsTTN. Takes named arguments.

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

Base.copy(params::OptimizeParamsTTN)

Shallow copy OptimizeParamsTTN.

function optimize!(sysenv::StateEnvsTTN,
                   params::OptimizeParamsTTN,
                   sweeppath::Vector{Int2};
                   kwargs...)

Performs optimization of the TTN.

Arguments:

• sysenv::StateEnvsTTN.
• params::OptimizationParamsTTN.
• sweeppath::Vector{Int2}: The path to be followed during optimization sweep. A vector that must contain all the nodes atleast once.

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 calculation. Must be set to greater than 0 for the excited state optimization.
• outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

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

Named arguments for eig_solver and their default values:

See documentation of KrylovKit.jl.

• ishermitian::Bool = true
• solver_tol::Float64 = 1E-14.
• solver_krylovdim::Int = 3.
• solver_maxiter::Int = 1.
• solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
• solver_eager::Bool = false.
• solver_check_convergence::Bool = false.

Return values:

• SweepDataTTN

function optimize(psi0::TTN, H::CouplingModel,
                  params::OptimizeParamsTTN,
                  sweeppath::Vector{Int2};
                  kwargs...)

function optimize(psi0::TTN, H::CouplingModel, Ms::Vector{TTN},
                  params::OptimizeParamsTTN,
                  sweeppath::Vector{Int2};
                  kwargs...)

Performs optimization of the TTN.

Arguments:

• psi0::TTN: Initial TTN.
• H::CouplingModel, Ms::Vector{MPS}.
• params::OptimizationParamsTTN.
• sweeppath::Vector{Int2}: The path to be followed during optimization sweep. A vector that must contain all the nodes atleast once.

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 calculation. Must be set to greater than 0 for the excited state optimization.
• outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

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

Named arguments for eig_solver and their default values:

See documentation of KrylovKit.jl.

• ishermitian::Bool = true
• solver_tol::Float64 = 1E-14.
• solver_krylovdim::Int = 3.
• solver_maxiter::Int = 1.
• solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
• solver_eager::Bool = false.
• solver_check_convergence::Bool = false.

Return values:

• ::Union{Float64, ComplexF64}: Energy. It is complex if ishermitian == false.
• ::TTN: The state psi.