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Laughlin-Metropolis

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What is this?

This is a simple python/cython code implementing the Metropolis Monte Carlo algorithm to sample configurations from the Laughlin wave function with an arbitrary number of quasiholes.

The program was developed by Tommaso Comparin and Elia Macaluso to produce some of the results reported in the following paper: Observing anyonic statistics via time-of-flight measurements [arXiv:1712.07940 cond-mat.quant-gas, by R. O. Umucalilar, E. Macaluso, T. Comparin, and I. Carusotto].

If you use this code in a scientific project, please cite the corresponding Zenodo entry:

@misc{tommaso_comparin_2018_1161969,
  author       = {Tommaso Comparin, Elia Macaluso},
  title        = {{tcompa/Laughlin-Metropolis: Laughlin-Metropolis}},
  year         = 2018,
  doi          = {10.5281/zenodo.1161969},
  url          = {https://doi.org/10.5281/zenodo.1161969}
}

How to use it?

This code requires the numpy and cython libraries, and it works on python 2.7, 3.4, 3.5 and 3.6. Elementary tests are available in the Tests folder, and they are performed at each commit (see the current status on https://travis-ci.org/tcompa/Laughlin-Metropolis). To run the examples, also the future and matplotlib libraries are needed.

Before being imported in a python script, the module lib_laughlin_metropolis.pyx has to be compiled through the command

$ python setup_cython.py build_ext --inplace

After this step, it can be imported in ordinary python scripts. Have a look at the example scripts (in the Examples folder):

  • In example_1_mean_square_radius.py, the average square radius is computed in several Monte Carlo runs.
  • In example_2_density_profile.py, the density profile is computed and shown, for parameters corresponding to Fig. 2(b) of the reference above [Umucalilar et al.].
  • In example_3_wigner_crystal.py, a Monte Carlo simulation is performed for a large value of m (where the system is in the Wigner-crystal phase), and the final configuration is shown.

Note on physical units

Within our program, the unit of length is defined such that

,

and the (non-normalized) probability distribution sampled with the Monte Carlo algorithm reads

.

License

MIT License

Copyright (c) 2018 Tommaso Comparin

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.