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

Andrea Pizzi, Johannes Knolle () and Andreas Nunnenkamp
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Andrea Pizzi: University of Cambridge
Johannes Knolle: Technische Universität München
Andreas Nunnenkamp: University of Nottingham

Nature Communications, 2021, vol. 12, issue 1, 1-7

Abstract: Abstract Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, 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.

Date: 2021
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DOI: 10.1038/s41467-021-22583-5

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