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Sweeping through the TTN

At a lower level of abstraction, TenNetLib.jl allows to control each fullsweep manually to update StateEnvsTTN.

Skip this part if you want to avoid lower-level abstraction.

SweepDataTTN

TenNetLib.jl defines a struct, called SweepDataTTN, to store essential data after each fullsweep.

TenNetLib.SweepDataTTN — Type
mutable struct SweepDataTTN
    sweepcount::Int
    maxchi::Vector{Int}
    energy::Vector{Union{Float64, ComplexF64}}
end

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

  • sweepcount::Int: Number of fullsweeps performed.
  • maxchi::Vector{Int}: Maximum MPS bond/link dimensions after every sweep.
  • energy::Vector{Union{Float64, ComplexF64}}: Energies after every sweep.

Default constructor:

  • SweepDataTTN(): Initialize an empty SweepData object.
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Base.copy — Method
Base.copy(swdata::SweepDataTTN)

Shallow copy of SweepDataTTN.

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sweeppath

TenNetLib.default_sweeppath — Function
function default_sweeppath(psi::TTN)

For a given a TTN having the default hierarchical binary tree structure, teturns the default path for sweeping through the TTN.

Return values:

  • Vector{Int2}: The list of nodes as the path to be followed during a (half)sweep.
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Perform a fullsweep

TenNetLib.fullsweep! — Method
function fullsweep!(sysenv::StateEnvsTTN, sweeppath::Vector{Int2}, solver,
                    swdata::SweepDataTTN; kwargs...)

Perform a fullsweep of the TTN by solver.

Arguments:

  • sysenv::StateEnvsTTN.
  • sweeppath::Vector{Int2}: The list of nodes as the path to be followed during a (half)sweep. Must have each node atleast once. For the next halfsweep the reverse path is followed.
  • solver: Solver for update. Currently only eig_solver is supported.
  • swdata::SweepDataTTN.

Named arguments and their default values:

  • time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for future functionality.
  • 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.
  • expand_dim::Int = 0 if noise == 0 else 20. Dimension to be expanded (on top of maxdim) during subspace expansion.
  • max_expand_dim::Int = 2 * expand_dim. maximum dimension to be expanded during subspace expansion.
  • expand_numiter::Int = 4. Number of iteration for subspace expansion. Should be greater than 1.
  • linkwise_maxdim::Union{Nothing, Dict{LinkTypeTTN, Int}} = nothing. Specifies maximum bond dimension of a particular link.
  • 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.
  • 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:

  • ::Union{Float64, ComplexF64}: Change in Energy ΔE. It is complex if ishermitian == false.

swdata::SweepDataTTN gets updated.

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