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

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...

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Published inNature communications Vol. 12; no. 1; pp. 2341 - 7
Main Authors Pizzi, Andrea, Knolle, Johannes, Nunnenkamp, Andreas
Format Journal Article
LanguageEnglish
Published London Nature Publishing Group UK 20.04.2021
Nature Publishing Group
Nature Portfolio
Subjects
639/766/119/2795
639/766/483/1139
Approximation
Crystals
Discrete time systems
Equilibrium
Hilbert space
Humanities and Social Sciences
Integers
Laboratories
Magnetic fields
multidisciplinary
Periodicity
Phases
Physics
Science
Science (multidisciplinary)
Symmetry
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Summary: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. Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions.
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ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-021-22583-5