Pre-thermal phases of matter protected by time-translation symmetry

TL;DR

This paper demonstrates that novel phases of matter protected by time-translation symmetry, including Floquet time crystals, can exist in the pre-thermal regime of driven systems without requiring disorder or integrability, and can persist for very long times.

Contribution

It proves the existence of pre-thermal phases protected by time-translation symmetry in driven systems, extending previous results to non-integrable and disordered systems, and constructs stationary systems breaking continuous time-translation symmetry.

Findings

Pre-thermal regimes persist for exponentially long times in drive frequency.

Floquet time crystals can exist without disorder or integrability.

Pre-thermal phases may persist indefinitely when coupled to a cold bath.

Abstract

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed "Floquet time crystals". We show that such phases of matter can exist in the pre-thermal regime of periodically-driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quenched disorder that limited previous constructions. We prove a theorem that states that such a pre-thermal regime persists until times that are nearly exponentially-long in the ratio of certain couplings to the drive frequency. By similar techniques, we can also construct stationary systems which spontaneously break *continuous* time-translation symmetry. We argue furthermore that for driven systems coupled to a cold bath, the pre-thermal regime could potentially persist to infinite time.