Long-Range Prethermal Phases of Nonequilibrium Matter

Abstract

We prove the existence of nonequilibrium phases of matter in the prethermal regime of periodically driven, long-range interacting systems, with power-law exponent α > d, where d is 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.

Long-Lived Interacting Phases of Matter Protected by Multiple Time-Translation Symmetries in Quasiperiodically Driven Systems

“…Considering our results and those of Ref. [130], we see that the analogs of power-law dependence of Fourier modes are interactions that decay as a power law in the number of sites contained within the support of the interaction. By contrast, Ref.…”

“…We can immediately combine our proof with the approach of Ref. [130] to derive similar results of slow heating and emergent symmetries in quasiperiodically driven systems with power-law interactions. These extensions are particularly valuable for realizing quasiperiodic phases in trapped ion systems, which naturally have long-range interactions.…”

“…The study of prethermalization in Floquet systems suggests that this restriction may be lifted to encompass long-range interactions. References [129,130] have demonstrated slow heating for periodic driving in the presence of two-body power-law interactions, provided that the interactions decay with distance as ∼1=r α , with α > d, where d is the spatial dimension; see also Ref. [131].…”

“…By contrast, Ref. [130] established results only for interactions that decay as a power law in the diameter of the support while still decaying exponentially in the number of sites.…”

“…(71), one invokes Lieb-Robinson bounds, following an identical argument as in Appendix D of Ref. [130] (but using the Lieb-Robinson bound for shortrange interactions). Equation 68follows immediately from the arguments in Ref.…”