Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation

TL;DR

Qsymm introduces efficient algorithms and a Python package for symmetry analysis and Hamiltonian generation, aiding research in topological phases and condensed matter physics.

Contribution

It provides the first deterministic polynomial-time algorithms for generating compatible Hamiltonians and identifying symmetries, applicable to all continuous and discrete symmetries.

Findings

Algorithms are numerically stable and deterministic.

Successfully applied to Majorana wires and Kekule graphene.

Demonstrates practical utility in condensed matter research.

Abstract

Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological phases. We address two converse questions relevant to the symmetry classification of systems: Is it possible to generate all possible single-body Hamiltonians compatible with a given symmetry group? Is it possible to find all the symmetries of a given family of Hamiltonians? We present numerically stable, deterministic polynomial time algorithms to solve both of these problems. Our treatment extends to all continuous or discrete symmetries of non-interacting lattice or continuum Hamiltonians. We implement the algorithms in the Qsymm Python package, and demonstrate their usefulness with examples from active research areas in condensed matter physics, including Majorana wires and Kekule graphene.