Source Code Documentation

By Jack Dunham

TimeEvolutionPEPO.jl is a high-level and domain-specific package for simulating the time-evolution of an open-quantum system represented by the iPEPO ansatz. A variety of options are implemented under one common interface for both Lindblad real-time evolution and thermal state annealing.

Keywords: Open Quantum Systems, Tensor Networks, Spins

Installation

To use this package, first create a new directory (or navigate to an existing directory) and start Julia from the command line:

mkdir MyProject
cd MyProject
julia

You should then activate an enviroment withing the directory to avoid polluting your global enviroment. First open the package manager interface by typing ] at the Julia prompt:

julia>]

Then from the package interface,

(@v1.11) pkg> activate .

which activates (or creates) an enviroment in current directory, indiciated by the .. Packages can then be added to this enviroment:

(MyProject) pkg> add TimeEvolutionPEPO

which will install the TimeEvolutionPEPO package, and add it to the enviroment. Note the change in prompt from (@v1.11) (the global enviroment) to (MyProject) (the local enviroment). Additional packages that might be useful can also be added:

(MyProject) pkg> add Plots, DataFrames

Code Example

function thermalising(; Jz = 1.0, D = 2)
    _, _, Z = PAULI

    # Spin-1/2 local Hilbert space dimension
    localdim = 2

    # Initialise to the infinite temperate thermal state on 2x2 unit cell lattice
    rho = PEPO(fill(ThermalState(),2,2), localdim, D)

    # Define the square lattice Ising model critical temperature
    βc = log(1 + sqrt(2)) / 2

    # Construct the anti-ferromagnetic Ising model
    model = Model(Jz * LocalOp(Z, Z))

    # Define a method, here we use time-evolving block decimation (TEBD) with default options
    method = TEBD()

    # We also need to define how we compute observables. Here we use the VUMPS algorithm
    obsalg = VUMPS(bonddim=16, maxiter=200, tol=1e-8)

    # We then set up the problem we wish to solve
    sim = Simulation(rho, model, method; timestep = 0.002 * βc)

    # Define an empty vector to store our output
    xis = Float64[]

    # Run the simulation!
    simulate!(sim; numsteps = 1000, maxshots=100) do simstep
        if simulationinfo(simstep).iterations == 0
            return nothing
        end

        # Compute the density matrix
        dm = DensityMatrix(quantumstate(simstep), obsalg)

        # Append the correlation length to the output vector
        push!(xis, correlationlength(dm))

        return nothing
    end

    return xis
end

Related Literature

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