Long-Range Prethermal Phases of Nonequilibrium Matter

We prove the existence of nonequilibrium phases of matter in the prethermal regime of periodically driven, long-range interacting systems, with power-law exponentα>d, wheredis the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension—a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpart.