Floquet Phases of Matter via Classical Prethermalization

TL;DR

This paper shows that classical many-body systems under periodic driving can exhibit nonequilibrium phases like time crystals during their prethermal regime, with emergent symmetries and long-lived subharmonic responses.

Contribution

It introduces the concept of classical prethermal time crystals and demonstrates their existence through theoretical proofs and numerical simulations, extending Floquet phase understanding.

Findings

Existence of classical prethermal time crystals

Emergent symmetries protected by discrete time-translation symmetry

Long-lived subharmonic response characteristic of time crystalline order

Abstract

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed.