Higher-order and fractional discrete time crystals in clean long-range interacting systems

Andrea Pizzi; Johannes Knolle; Andreas Nunnenkamp

doi:10.1038/s41467-021-22583-5

paper

Higher-order and fractional discrete time crystals in clean long-range interacting systems

arXiv:1910.07539 · doi:10.1038/s41467-021-22583-5

Abstract

Discrete time crystals are periodically driven systems characterized by a response with periodicity $n T$ , with $T$ the period of the drive and $n > 1$ . Typically, $n$ is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin- $1/2$ systems with $n$ restricted to $2$ . Here we show that a clean spin- $1/2$ system in the presence of long-range interactions and transverse field can sustain a huge variety of different `higher-order' discrete time crystals with integer and, surprisingly, even fractional $n > 2$ . We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.

6+6 pages, 4+2 figures

Higher-order and fractional discrete time crystals in clean long-range interacting systems

Abstract

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