Floquet Time Crystals

TL;DR

This paper defines spontaneous breaking of time translation symmetry in quantum systems and demonstrates its occurrence in many-body-localized driven systems through analytical and numerical methods.

Contribution

It introduces a formal definition of time translation symmetry breaking and provides evidence for its realization in specific quantum models.

Findings

Time translation symmetry can be spontaneously broken in quantum systems.

Many-body localization supports the existence of time crystals.

Numerical simulations confirm the theoretical predictions.

Abstract

We define what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.