Perform local updates

function update_position!(sysenv::StateEnvsTTN, solver, node::Int2;
                          time_step::Union{Float64, ComplexF64, Nothing},
                          normalize::Bool,
                          maxdim::Int,
                          mindim::Int,
                          cutoff::Float64,
                          svd_alg::String,
                          kwargs...)

Moves the orthogonality center to pos and update StateEnvsTTN at position pos by solver.

Arguments:

• sysenv::StateEnvsTTN
• solver: Solver for update. Currently only eig_solver is supported.
• pos::Int: Position of the node to be updated.

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".

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}: Energy. It is complex if ishermitian == false.

function subspace_expand!(psi::TTN, node::Int2, nextnode::Int2,
                          max_expand_dim::Int, noise::Float64)

Enlarges the bond domension between node and nextnode by max_expand_dim using the subspace expansion. The parameter noise controls stength of the perturbation.