Thermalization mechanism for time-periodic finite isolated interacting quantum systems

TL;DR

This paper develops a theory explaining how finite isolated quantum systems with periodic driving thermalize over time, linking long-term behavior to an effective Hamiltonian and confirming predictions with numerical simulations.

Contribution

It introduces a thermalization mechanism for periodically driven quantum systems, connecting Floquet states to eigenstate thermalization hypothesis and validating with Bose-Hubbard model simulations.

Findings

Long-time observables relate to an effective Hamiltonian.

Systems thermalize if the effective Hamiltonian is nonintegrable.

Numerical results agree with theoretical predictions.

Abstract

We present a theory to describe thermalization mechanism for time-periodic finite isolated interacting quantum systems. The long time asymptote of natural observables in Floquet states is directly related to averages of these observables governed by a time-independent effective Hamiltonian. We prove that if the effective system is nonintegrable and satisfies eigenstate thermalization hypothesis, quantum states of such time-periodic isolated systems will thermalize. After a long time evolution, system will relax to a stationary state, which only depends on an initial energy of the effective Hamiltonian and follows a generalized eigenstate thermalization hypothesis. A numerical test for the periodically modulated Bose-Hubbard model, with the extra nearest neighbor interaction on the bosonic lattice, agrees with the theoretical predictions.