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 that do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new nonequilibrium 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 nonequilibrium phenomenon that is stabilized by many-body interactions, with no analog in noninteracting systems. We explain the theory behind several proposed models of discrete time crystals, and compare several recent realizations, in different experimental contexts.
Discrete time crystals in Bose-Einstein condensates and the symmetry-breaking edge in a simple two-mode theory
