Quantum and classical Floquet prethermalization

TL;DR

Floquet prethermalization allows many-body systems under high-frequency periodic driving to avoid heating and exhibit interesting transient physics, with rigorous theoretical foundations and experimental observations across quantum and classical models.

Contribution

This review consolidates current understanding of Floquet prethermalization, including rigorous theorems, extensions to unbounded systems, and applications to nonequilibrium phases and quantum simulators.

Findings

Rigorous theorems for quantum spin and fermionic systems

Suppression of heating rate at high driving frequencies

Experimental evidence of prethermalization phenomena

Abstract

Time-periodic (Floquet) driving is a powerful way to control the dynamics of complex systems, which can be used to induce a plethora of new physical phenomena. However, when applied to many-body systems, Floquet driving can also cause heating, and lead to a featureless infinite-temperature state, hindering most useful applications. It is therefore important to find mechanisms to suppress such effects. Floquet prethermalization refers to the phenomenon where many-body systems subject to a high-frequency periodic drive avoid heating for very long times, instead tending to transient states that can host interesting physics. Its key signature is a strong parametric suppression of the heating rate as a function of the driving frequency. Here, we review our present understanding of this phenomenon in both quantum and classical systems, and across various models and methods. In particular, we present rigorous theorems underpinning Floquet prethermalization in quantum spin and fermionic lattice systems, extensions to systems with degrees of freedom that have unbounded local dimension. Further, we briefly describe applications to novel nonequilibrium phases of matter, and recent experiments probing prethermalization with quantum simulators. We close by describing the frontiers of Floquet prethermalization beyond strictly time-periodic drives, including time-quasiperiodic driving and long-lived quasi-conserved quantities enabled by large separation of energy scales.