/markovian_closure_fermions

Primary LanguageJuliaGNU General Public License v3.0GPL-3.0

Fermionic Markovian closure

This repository contains the code used for the simulations in [1]. There are some scripts computing the evolution of several types of physical systems, employing the Markovian closure technique as explained in the article.

Installation

First of all, clone this repository on your computer. The Project.toml file lists all the packages you need. Some of them are personal packages which are not listed in Julia's general registry, but in this one. Add the registry by running, in a Julia interactive session,

using Pkg
pkg"registry add https://github.com/phaerrax/TensorNetworkSimulations.git"

Now you can download all the required packages:

using Pkg
pkg"instantiate"

Description of the repository

In this repository you will find:

  • some Julia scripts which perform the simulation of some physical models such as the SIAM (siam) or a quantum dot impurity (qdot), either using a standard TEDOPA method (pure….jl) or the Markovian closure (mc….jl);
  • an example folder which contains the parameter files of some concrete simulations, as well as some frequently used spectral densities.
  • a mc_standard_parameters which contains the parameters needed for the implementation of the Markovian closure technique in the simulation scripts;
  • some Julia scripts that calculate the chain coefficients, in several ways, starting from the data of a spectral density (chainmapping_….jl);
  • a folder TimeEvoVecMPS, a self-contained Julia package (imported by every script) which defines functions for the various flavours of the TDVP algorithm and some other utilities for the simulations.

How it works

The parameters for each simulation script must be supplied, in a JSON file, as the first (and only) command-line argument. You can find some examples in the test/spectral_densities directory. Please note that the script that computes the thermofield coefficients currently works only if the chemical potential is zero (this does not affect the generality of our algorithms, since any spectral density can always be shifted so that its chemical potential is zero), so for now care must be taken to write the parameter files according to this specification. All files in test/spectral_densities already follow this convention. In order to run a simulation script, run from the base folder (i.e. the root of the Git repository)

julia --project <script.jl> <parameter_file.json>

using the full relative paths of the files, e.g.

julia --project siam/spinless/mc.jl test/siam/spinless/mu1/NE8/mc60_NC6.json

Example

Here is an example of a complete workflow, starting from scratch. We want to simulate a spinless SIAM with some given parameter files: test/spectral_densities_semicircle_T4_mu0.5.json representing a semicircle spectral density, and examples/siam_mc.jl with the parameters for the physical simulation of the model with a Markovian closure.

  1. Generate the thermofield coefficients from the spectral density, with
julia --project chainmapping_thermofield.jl examples/spectral_densities/semicircle_T4_mu0.5.json

The output is a file called test/spectral_densities/semicircle_T4_mu0.5.thermofield, which will be called later in examples/siam_mc.json in the chain_coefficients entry. It is not necessary to generate the coefficient each time, if the file already exists. 2. Run the simulation script with

julia --project siam/spinless/mc.jl examples/siam_spinless_mc.json

Note that the parameter file examples/siam_mc.json also specifies some output files which will contain the expectation values of the given observables, an HDF5 file containing the final state, and so on. If one does not need such results, /dev/null or an equivalent destination may be given to avoid creating unnecessary output files.

The examples directory contains other sample parameter files that can be used with other simulation scripts:

julia --project siam/spinless/pure.jl examples/siam_spinless_pure.json
julia --project siam/spinful/mc.jl examples/siam_spinful_mc.json
julia --project qdot/mc_2l.jl examples/qdot_2levels_mc.json

Common parameters and their meaning

  • Chain coefficients:

    • chain_coefficients: a file containing the chain coefficients
    • chain_length: an integer specifying how many sites to keep in the environment chains before attaching the closure

  • Output files:

    • out_file: expectation values of observables
    • state_file: final MPS (in HDF5 format)
    • ranks_file: bond dimensions of the MPS, step by step
    • times_file: wall-clock time needed for each evolution step

  • Integration parameters for the simulation:

    • tmax: final (physical) time of the simulation
    • tstep: integration time step
    • ms_stride: measure observables only each ms_stride steps
    • max_bond: maximum bond dimension for the MPS
    • discarded_w: cutoff for MPS truncation during the evolution

  • Observables:

    • observables: a vector specifying the name of the observable (a valid ITensor operator) and a list of sites on which it will be measured, e.g.

      {
    "vN":  [1,2,3,10,11,16,17],
    "vX":  [1,2,3,4]
}

    (note that the v prefix here is used for the "vectorized fermion" systems --- please consult the LindbladVectorizedTensors package documentation for more information)

  • Markovian closure parameters:

    • MC_alphas: mc_standard_parameters/alphas_6.dat,
    • MC_betas: mc_standard_parameters/betas_6.dat,
    • MC_coups: mc_standard_parameters/coupls_6.dat

    These are already existing files. You only need to change the number in the file name from 6 to 8 or 10 if you want to use closures with a different number of modes.

  • Other system-specific parameters, e.g. when the open system is a two-level system (a fermion, maybe) we need:

    • sys_en: energy of the open system
    • sys_ini: initial state of the open system

Documentation

The TimeEvoVecMPS package, included in this repo, has its own documentation (still a work in progress), which is not yet hosted and must be generated manually: from the docs directory, run julia --project make.jl and wait for the command to end. You will then be able to access the documentation from docs/builds/index.html, by opening it from any Web browser.

References

[1] Ferracin, D., Smirne, A., Huelga, S. F., Plenio M. B. and Tamascelli, D. (2024). Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments. arxiv.org/abs/2407.10017.