Floquet Thermalization: Symmetries and Random Matrix Ensembles

TL;DR

This paper explores how symmetries influence the random matrix classification of quantum thermalization in periodically driven systems, revealing that Floquet systems can differ from their instantaneous Hamiltonians in symmetry class and thermalization behavior.

Contribution

It demonstrates that Floquet systems can belong to different random matrix classes than their instantaneous Hamiltonians and can thermalize independently of the Hamiltonian's integrability.

Findings

Floquet systems can be in different symmetry classes than instantaneous Hamiltonians.

A Floquet system can thermalize even if the instantaneous Hamiltonian is integrable.

Crossovers between random matrix classes occur as a function of driving frequency.

Abstract

We investigate the role of symmetries in determining the random matrix class describing quantum thermalization in a periodically driven many body quantum system. Using a combination of analytical arguments and numerical exact diagonalization, we establish that a periodically driven `Floquet' system can be in a different random matrix class to the instantaneous Hamiltonian. A periodically driven system can thermalize even when the instantaneous Hamiltonian is integrable. A Floquet system that thermalizes in general can display integrable behavior at commensurate driving frequencies. When the instantaneous Hamiltonian and Floquet operator both thermalize, the Floquet problem can be in the unitary class while the instantaneous Hamiltonian is always in the orthogonal class, and vice versa. We extract general principles regarding when a Floquet problem can thermalize to a different symmetry class to the instantaneous Hamiltonian. A (finite-sized) Floquet system can even display crossovers between different random matrix classes as a function of driving frequency.