Stroboscopic prethermalization in weakly interacting periodically driven systems

TL;DR

This paper demonstrates that weakly interacting periodically driven quantum systems can exhibit a prethermalized state with synchronized dynamics over many periods before heating to infinite temperature, supported by numerical simulations.

Contribution

It introduces the concept of stroboscopic prethermalization in weakly non-integrable systems, showing a separation of timescales for synchronization and thermalization.

Findings

Quasi-periodic evolution persists over many periods

Synchronized states are described by approximate constants of motion

Numerical simulations confirm the theoretical predictions

Abstract

Time-periodic driving provides a promising route to engineer non-trivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable systems can synchronize with the driving into a non-trivial periodic motion, generic non-integrable systems are expected to heat up until they display a trivial infinite-temperature behavior. In this paper we show that a quasi-periodic time evolution over many periods can also emerge in systems with weak integrability breaking, with a clear separation of the timescales for synchronization and the eventual approach of the infinite-temperature state. This behavior is the analogue of prethermalization in quenched systems. The synchronized state can be described using a macroscopic number of approximate constants of motion. We corroborate these findings with numerical simulations for the driven Hubbard model.