Example for *moller* calculation with DSQSS
---------------------------------------------

What’s this sample?
~~~~~~~~~~~~~~~~~~~~~~~

This is an example of ``moller`` with
`DSQSS <https://github.com/issp-center-dev/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
:math:`\chi` of the :math:`S=1/2` (:math:`M=1` in the terms of DSQSS)
and :math:`S=1` (:math:`M=2`) antiferromagnetic Heisenberg chain under
the periodic boundary condition with several length. By using
``moller``, calculations with different parameters (:math:`M, L, T`) are
performed in parallel.

This example is corresponding to `one of the official
tutorials <https://issp-center-dev.github.io/dsqss/manual/develop/en/dla/tutorial/spinchain.html>`__.

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.

   .. code:: bash

      $ 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``.

   .. code:: bash

      $ 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.

   .. code:: bash

      $ sbatch job.sh list.dat

4. Check status

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

   .. code:: bash

      $ moller_status input.yaml list.dat

5. Gather results

   After calculation finishes, gather result by

   .. code:: bash

      $ python3 ../extract_result.py list.dat

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

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

   .. code:: bash

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

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

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

.. |susceptibilities for S=1/2| image:: ../../../../images/tutorial_dsqss_M1.*
.. |susceptibilities for S=2| image:: ../../../../images/tutorial_dsqss_M2.*