3.3. Example for moller calculation with DSQSS

What’s this sample?

This is an example of moller with DSQSS, which is an open-source software package for performing the path-integral Monte Calro method for quantum many-body problem. In this example, we will calculate the temperature dependence of the magnetic susceptibilities \(\chi\) of the \(S=1/2\) (\(M=1\) in the terms of DSQSS) and \(S=1\) (\(M=2\)) antiferromagnetic Heisenberg chain under the periodic boundary condition with several length. By using moller, calculations with different parameters (\(M, L, T\)) are performed in parallel.

This example is corresponding to one of the official tutorials.

Preparation

Make sure that moller (HTP-tools) package and DSQSS are installed. In this tutorial, the calculation will be performed using the supercomputer system ohtaka at ISSP.

How to run

  1. Prepare dataset

    Run the script make_inputs.sh enclosed within this package.

    $ bash ./make_inputs.sh

    This make an output directory (if already exists, first removed then make again). Under output, working directories for each parameter like L_8__M_1__T_1.0 will be generated. A list of the directories is written to a file list.dat.

  2. Generate job script using moller

    Generate a job script from the job description file using moller, and store the script as a file named job.sh.

    $ moller -o job.sh input.yaml

    Then, copy job.sh in the output directory, and change directory to output.

  3. Run batch job

    Submit a batch job with the job list as an argument.

    $ sbatch job.sh list.dat

  4. Check status

    The status of task execution will be summarized by moller_status program.

    $ moller_status input.yaml list.dat

  5. Gather results

    After calculation finishes, gather result by

    $ python3 ../extract_result.py list.dat

    This script writes results into a text file result.dat which has 5 columns, \(M\), \(L\), \(T\), mean of \(\chi\), and stderr of \(\chi\).

    To visualize the results, GNUPLOT files plot_M1.plt and plot_M2.plt are available.

    $ gnuplot --persist plot_M1.plt
$ gnuplot --persist plot_M2.plt

    susceptibilities for S=1/2 susceptibilities for S=2

    The main different between \(S=1/2\) and \(S=1\) AFH chains is whether the excitation gap vanishes (\(S=1/2\)) or remains (\(S=1\)). Reflecting this, the magnetic susceptibility in the very low temperature region remains finite (\(S=1/2\)) or vanishes (\(S=1\)). Note that for the \(S=1/2\) case, the finite size effect opens the spin gap and therefore the magnetic susceptibility of small chains drops.