Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit

TL;DR

This paper explores prethermalization in periodically driven many-body systems at intermediate to low frequencies, demonstrating long-lived prethermal states, their stability, and the role of inverse-frequency expansion in describing thermalization processes.

Contribution

It extends the understanding of prethermalization beyond high-frequency limits using numerical evidence and effective Floquet Hamiltonians, revealing new scaling behaviors and thermalization mechanisms.

Findings

Prethermal plateau formation at intermediate frequencies.

Stability of prethermal states against drive perturbations.

Various heating rate scalings depending on drive conditions.

Abstract

We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability w.r.t.~random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are non-universal: we observe Fermi's Golden Rule scaling, power-law scaling inconsistent with the Golden Rule, and non-power law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.