Asymptotic prethermalization in periodically driven classical spin chains

Abstract

We reveal a novel continuous dynamical heating transition between a prethermal and an infinite-temperature phase in a clean, chaotic periodically-driven classical spin chain. The transition time is a steep exponential function of the driving frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Despite the inapplicability of Floquet's theorem to nonlinear systems, we present strong evidence that the physics of the prethermal phase is described well by the inverse-frequency expansion, even though its stability and robustness are related to drive-induced coherence not captured by the expansion. Our results pave the way to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for cold atom experiments in the superfluid regime.