sse
Implementation of Stochastic Series Expansion Monte Carlo method for the spin-S XXZ model. https://doi.org/10.1103/PhysRevE.67.046701
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Implementation of Stochastic Series Expansion Monte Carlo method for the spin-S XXZ model. https://doi.org/10.1103/PhysRevE.67.046701
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README.md
Stochastic Series Expansion - SSE
Please cite the code uising the citation file provided in the repository. https://doi.org/10.5281/zenodo.10034200
Implementation of Stochastic Series Expansion (SSE) Monte Carlo method for the spin-S XXZ model. This version uses the Directed Loops [1] method for the loop update. The Hamiltonian of the simulated system is given by
$$ H = J \sum{\langle i, j \rangle} \left[ \frac{1}{2} (S^+i S^-j + S^-i S^+j) + \Delta S^zi S^zj \right] - h \sumi S^z_i $$
where $J$ is the coupling constant, $\Delta$ is the magnetic anisotropy along the $z$-direction and $h$ is an external magnetic field. In the code, $J = 1$, then if $\Delta > 0$ the system is antiferromagnetic and if $\Delta < 0$ the system is ferromagnetic. The SSE method is the power series expansion of the partition function
$$ Z = \text{Tr}{e^{-\beta H}} = \sum{\alpha} \sum{n=0}^{\infty} \frac{(-\beta)^n}{n!} \langle \alpha |H^n| \alpha \rangle $$
where $\beta \equiv 1 / T$.
The implementation uses binnig for the estimation of the standard deviations of the sampled quantities. It is possible to run each bin in parallel mode, using openMP.
Usage
To use and run the implementation, it is required that you have a C and fortran90 compilers and a version of Python3 installed with numpy.
To compile the code, run
bash
$ source build.sh
in the main directory. This will compile the code and set the enviroment variable $SSE_DIR. To run the code, create a new directory and copy the parameter file (found in scripts_and_parameters/Start/) to the directory and type
bash
$ $SSE_DIR/src/main n_threads $SSE_DIR
This will run the a SSE simulation with the paramertes specified in the parameter file using n_threads threads. To analyse the observables,
bash
$ $SSE_DIR/src/ana obs_1 obs_2 ...
[1] - "Directed loop updates for quantum lattice models", Olav F. Syljuåsen, 2003, Phys. Rev. E 67, 046701, https://doi.org/10.1103/PhysRevE.67.046701
Owner
- Name: João Inácio
- Login: joaogci
- Kind: user
- Location: Germany
- Company: Universität Würzburg
- Repositories: 1
- Profile: https://github.com/joaogci
PhD fellow @ Würzburg
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!
cff-version: 1.2.0
title: SSE for 1D spin-S XXZ model
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
authors:
- given-names: João
family-names: Carvalho Inácio
email: inacio.joao@proton.me
identifiers:
- type: url
value: 'https://github.com/joaogci/SSE'
repository-code: 'https://github.com/joaogci/SSE'
abstract: >-
Implementation of Stochastic Series Expansion (SSE) Monte
Carlo method for the spin-S XXZ model.
keywords:
- stochastic-series-expansion
- quantum-monte-carlo
- quantum-spin-model
- xxz-model
license: MIT
commit: 93fd676
version: '1'
date-released: '2023-07-21'
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