BIOMS: Binary Integrals of Motion

BIOMS is a small python package for constructing quantum operators that are approximate binary integrals of motion. It is built on top of the QOSY python package.

We used BIOMS to study many-body localization (MBL) in one, two, and three-dimensions by finding binary integrals of motion known as "localized bits", or l-bits [1].

Features

BIOMS implements a heuristic algorithm that takes as input an operator H (such as a Hamiltonian) and produces as output an operator O that minimizes the sum of the binarity |O^2 - I|^2 and the commutator norm |[H, O]|^2.

The bioms folder contains our implementation of the algorithm.

The runs folder contains our code for using BIOMS to find approximate l-bits in 1D, 2D, and 3D systems.

Getting Started

Prerequisites

BIOMS requires the following software installed on your platform:

• Python 3
• Numpy
• Scipy
• QOSY
• If you want to run the tests: pytest

Installing

To copy the development version of the code to your machine, type

git clone https://github.com/ClarkResearchGroup/bioms.git

To install, type

cd bioms
python setup.py install --user

or add the bioms folder to your PYTHONPATH environment variable.

Testing

To test BIOMS after installation (recommended), type

cd bioms/tests
pytest

Authors

• Eli Chertkov

License

This project is licensed under the MIT License - see the LICENSE for details.

References

BIOMS is introduced in the following study of MBL in greater than one dimensions:

[1] E. Chertkov, B. Villalonga, and B. K. Clark, “Numerical evidence for many-body localization in two and three dimensions,” arXiv:2007.02959 (2020).

Qosy is based on work presented in

[2] E. Chertkov, B. Villalonga, and B. K. Clark, “Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach,” Phys. Rev. Research 2, 023348 (2020).