Prethermal Phases of Matter Protected by Time-Translation Symmetry

Dominic V Else,Bela Bauer,Chetan Nayak

doi:10.1103/physrevx.7.011026

Dominic V Else, Bela Bauer + Show 1 more

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https://doi.org/10.1103/physrevx.7.011026

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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.

Highlights

Much of condensed matter physics revolves around determining which distinct phases of matter can exist as equilibrium states of physical systems
We show that prethermal systems can exhibit phases of matter that cannot exist in thermal equilibrium
We construct prethermal “Floquet time crystals,” which spontaneously break the discrete time-translation symmetry of periodically driven systems [43]. (For an alternative view of such systems that focuses on other symmetries of the discrete time-translation operator, see Refs. [29,44,45].) Floquet time crystals are the focus of this paper, but as a by-product of our analysis, we find prethermal—i.e., nonequilibrium—time crystals that spontaneously break continuous time-translation symmetry

Summary

Introduction

Much of condensed matter physics revolves around determining which distinct phases of matter can exist as equilibrium states of physical systems. A set of uniquely quantum phases—symmetry-protected topological (SPT) phases [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19], including topological insulators [20,21], and symmetry-enriched topological (SET) phases [22,23,24,25,26,27,28]— has been discovered These phases, while symmetric, manifest the symmetry in subtly anomalous ways and are distinct only as long as the symmetry is preserved. We can collectively refer to these three classes of phases as symmetry-protected phases of matter

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