Settn.jl

A prototype of the series-expansion thermal tensor network (SETTN) algorithm [PRB 95, 161104] is illustrated for the XY chain. Other models can be easily customized thanks to ITensors.jl's OpSum function.

This package is also an essential ingredient for more advanced thermal tensor network algorithms, such as XTRG and tanTRG. In particular, two-site variational MPO sum and product discussed in PRB 95, 161104 and PRX 8, 031082 are implemented, which can be used in other modules via:

using SETTN: +, contract

julia> ] add Settn

To make it minimal, this package only exports two functions,

"""
function get_ρ(H::MPO, β::Float64; kwargs...) -> ρ::MPO

    calculate density matrix ρ(β) using SETTN algorithm
"""
function get_ρ(H::MPO, β::Float64; kwargs...)

and

"""
function get_fe(ρ::MPO, β::Float64) -> fe::Float64

    calculate free energy at β given ρ(β/2) and β
"""
function get_fe(ρ::MPO, β::Float64)

Check the examples/ directory for computing free energy of the XY chain:

julia> cd("examples")
julia> using Pkg
julia> Pkg.instantiate()
julia> include("test.jl")

Two-site variational MPO sum + and product contract, are extensions from ITensors.jl with ::Algorithm"variational", more details can be found in ./src/mpo.jl; also check the relevant part of source code in ITensors.jl package. Note the sweep scheme for variational sum and product follows the same one for ITensors.jl's dmrg function.

• Implement a more numerically stable MPO product, such as the one given in PRB 102, 035147