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BoseHubbardGutzwiller

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What is this?

This is a simple python/cython code implementing the homogeneous Gutzwiller variational wave function for the Bose-Hubbard model. The search for the optimal wave-function parameters is performed through Simulated Annealing, a Monte Carlo method for stochastic optimization.

The program was developed to produce the Gutzwiller phase diagram reported in: Density-dependent hopping for ultracold atoms immersed in a Bose-Einstein-condensate vortex lattice [arXiv:1711.10234 cond-mat.quant-gas], by R. H. Chaviguri, T. Comparin, M. Di Liberto, and M. A. Caracanhas.

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

@misc{tommaso_comparin_2017_1067968,
  author       = {Tommaso Comparin},
  title        = {tcompa/BoseHubbardGutzwiller v1.0.2},
  year         = 2017,
  doi          = {10.5281/zenodo.1067968},
  url          = {https://doi.org/10.5281/zenodo.1067968}
}

How to use it?

This code requires the numpy and cython libraries (plus the future library, if you need to run the tests), and it is working 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/BoseHubbardGutzwiller).

Before being imported in a python script, the module lib_gutzwiller_simulated_annealing.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 two example files:

  • In example_1.py, a single simulated-annealing run is performed, and the energy and density are computed (using the optimized Gutzwiller coefficients).
  • In example_2.py, a scan of different J values is performed, showing the transition from a Mott insulator (integer density) to a superfluid.

Notes

  1. The user should play around with values of the simulated-annealing parameters. For instance a large value of the cooling rate might increase the chance of hitting local minima. An additional check consists in comparing the outcome of several independent runs (each one starting with a different initial condition for the Gutzwiller coefficients).
  2. If necessary, the code can easily be optimized further. An example of a possible change is to use the gsl random-number generator (see here), which is not implemented in this version to avoid an additional dependency.

License

MIT License

Copyright (c) 2017 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.