Discrete time crystals in long-range interacting systems

A generic periodically driven, isolated system will absorb energy until it looks, locally, like an infinite-temperature state. However, when the drive frequency is large compared with the local energy scales of the system, then the system can only absorb energy from the drive by spreading it out over many excitations. Consequently, heating occurs very slowly, and there is a long-lived quasi-steady state - a so-called "pre-thermal" state - in which ordered phases of matter can occur. In this context, I will describe how long-range interactions can stabilize pre-thermal time-translation symmetry breaking in one dimensional systems (even in the absence of disorder). I will begin by motivating a new definition for light-cones in power-law interacting quantum systems and using this definition, I will prove that long-range, pre-thermal time crystals naturally exhibit exponentially long lifetimes. Finally, an experimental realization of a one dimensional, pre-thermal time crystal in trapped atomic ions will be discussed.