# Discrete Time Crystals

## TL;DR

This review discusses the emergence of discrete time crystals, a novel non-equilibrium phase of matter characterized by spontaneously broken discrete time translation symmetry, stabilized by many-body interactions in isolated quantum systems.

## Contribution

It provides a comprehensive overview of the theoretical models and experimental realizations of discrete time crystals, highlighting their unique non-equilibrium properties.

## Key findings

- Discrete time crystals exhibit spontaneous breaking of discrete time symmetry.
- They are stabilized by many-body interactions, with no non-interacting analog.
- Recent experiments have successfully realized discrete time crystals in various contexts.

## Abstract

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on "discrete time crystals", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts.