Computing Floquet Hamiltonians with Symmetries

Abstract

Unitary matrices arise in many ways in physics, in particular as a time evolution operator. For a periodically driven system one frequently wishes to compute a Floquet Hamilonian that should be a Hermitian operator $H$ such that $e^{-iTH}=U(T)$ where $U(T)$ is the time evolution operator at time corresponding the period of the system. That is, we want $H$ to be equal to $-i$ times a matrix logarithm of $U(T)$. If the system has a symmetry, such as time reversal symmetry, one can expect $H$ to have a symmetry beyond being Hermitian. We discuss here practical numerical algorithms on computing matrix logarithms that have certain symmetries which can be used to compute Floquet Hamiltonians that have appropriate symmetries. Along the way, we prove some results on how a symmetry in the Floquet operator $U(T)$ can lead to a symmetry in a basis of Floquet eigenstates.

arXiv comment25 pages, 13 figure, 14 ancillary files, primarily Matlab files. Updated to have correct spelling of author names of authors in the Arxiv metadata

References in corpus (5)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Floquet Thermalization: Symmetries and Random Matrix Ensembles
• Computing a logarithm of a unitary matrix with general spectrum
• Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

Cited by in corpus (3)

• An operator-based approach to topological photonics
• Sparse system identification by low-rank approximation
• Quantitative measure of topological protection in Floquet systems through the spectral localizer