Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation

Varjas, D.; Rosdahl, T.O.; Akhmerov, A.R.

doi:10.1088/1367-2630/aadf67

Qsymm

Title

Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation

Author

Varjas, D. (TU Delft QuTech Advanced Research Centre; TU Delft QRD/Kouwenhoven Lab)
Rosdahl, T.O. (TU Delft QN/Akhmerov Group)
Akhmerov, A.R. (TU Delft QN/Akhmerov Group)

Date

2018

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.

Subject

grapheme
Majorana wire
SPT
symmetry

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http://resolver.tudelft.nl/uuid:d80c2482-f1d5-43d3-82e8-a3859a297597

DOI

https://doi.org/10.1088/1367-2630/aadf67

ISSN

1367-2630

Source

New Journal of Physics, 20 (9)

Part of collection

Institutional Repository