Source codes for implementation of the Kitaev Honeycomb model and related calculations.

This package was developed for research published in arXiv:2003.07280 .

• examples/example.ipynb

  Examples in Jupyeter notebooks

  Some basic examples of using built-in functions are demonstrated in examples/example.ipynb.

• source/show.py

  • a utility script to show .log file generated by netket, either gui or cui
  • see more usages with ./show.log --help

• source/honeycomb.py

  • some utility functions which will be used in many other codes. It includes, get_graph(), get_hamiltonian(), exact_diag(), gs_energy(), rbm(), measure() and flip_spins().
  • get_graph() is the most useful one. It generates an arbitary size honeycomb graph.
  • get_hamiltonian() uses get_graph() to get the Hamiltonian for an arbitary size honeycomb model.
  • after creating hamiltonian(by get_hamiltonian) and machine(derictly use netket), pass them into rbm() to train it.
  • exact_diag() gets energy level by directly diagnolize. gs_energy() gets gs energy by the analytic formula.
  • measure() is actually a lr=0 rbm().
  • flip_spins() manages to flip a spin by modifing parameters of an rbm.
  • This script is supposed to only be imported and used in other scripts. See contents of calc_gs.py as an example.

• source/calc_gs.py

  • use honeycomb.py to calc gs.

• source_torch/honeycomb.py

  • The conterpart of honeycomb.py in "source/honeycomb.py". Including
    • gen_H(): generate a Hamiltonian. Used in rbm_2x2.py.
  • add other varieties to support torch: gen_ops_npmat, gen_ops_torchsparse, gen_H_torchsparse, gen_shift_sym.

• source_torch/rbm_eig.py

  • Exact diagnolize Hamiltonian

• source_torch/rbm_2x2.py

  • Scripts for 2x2 lattice.
  • Esay to understand.

• source_torch/rbm_3x3.py

  • Scripts for 3x3 lattice.
  • "Projection method" and "pre-train technology" are used.

• source_torch/Full-36-14.275.pkl

  • network data for an rbm which can achieve -14.275 for 3x3 honeycomb model.

• source_torch/operators_3x3

  • Operators for 3x3 lattice.

In order to cite this work, use the following:

```
@misc{noorm2020restricted,
	title={Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model},
	author={Mohammadreza Noormandipour and Youran Sun and Babak Haghighat},
	year={2020},
	eprint={2003.07280},
	archivePrefix={arXiv},
	primaryClass={cond-mat.dis-nn}
}
```

We tried both NetKet and PyTorch. PyTorch is easy to install but NetKet is not. To install NetKet, you can try

• Build the conda environment using installation/environment.yml and activate it:

  conda env create -f environment.yml
  conda activate tqc
  

• Install mpich and then NetKet:

  pip install netket
  

• Use the docker file docker_tqc.