Abstract
Symmetry is a guiding principle in physics that allows us to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role by protecting 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 through applications in active research areas of condensed matter physics, including Majorana wires and Kekule graphene.
Highlights
A transformation that leaves a physical system invariant is called a symmetry, and such transformations have an ever-important role in modern physics
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
Analysis of condensed matter systems is commonly based on single-particle Hamiltonians, the symmetry properties and classification of which are crucial to understanding the physical properties
Summary
Original content from this work may be used under the terms of the Creative Abstract. Symmetry is a guiding principle in physics that allows us to generalize conclusions between many. In the ongoing search for new topological phases of matter, symmetry plays a crucial this work must maintain attribution to the role by protecting topological phases. We address two converse questions relevant to the symmetry author(s) and the title of classification of systems: is it possible to generate all possible single-body Hamiltonians compatible the work, journal citation and DOI. Is it possible to find all the symmetries of a given family of Hamiltonians? We implement the algorithms in the Qsymm Python package, and demonstrate their usefulness through applications in active research areas of condensed matter physics, including Majorana wires and Kekule graphene
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