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  • Letter
  • Open Access

Solvable model for discrete time crystal enforced by nonsymmorphic dynamical symmetry

Zi-Ang Hu1, Bo Fu1, Xiao Li2,3, and Shun-Qing Shen1,*

  • 1Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
  • 2Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, China
  • 3City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, Guangdong, China

  • *sshen@hku.hk
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Phys. Rev. Research 5, L032024 – Published 18 August, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032024

Abstract

Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with a system with nonsymmorphic dynamical symmetry, in which the instantaneous eigenstates become Möbius twisted, hence doubling the period of the instantaneous state. The exact solution of the time-dependent Schrödinger equation shows that the system spontaneously exhibits a period expansion without undergoing quantum superposition states for a series of specific evolution frequencies or in the limit of a long evolution period. In this case, the system gains a π Berry phase after two periods' evolution. While the instantaneous energy state is subharmonic to the system, the interaction will trigger off decoherence and thermalization that stabilize the oscillation pattern.

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Phys. Rev. Research 5, L032024– Published 18 August, 2023
  • Received 5 January 2023
  • Revised 9 May 2023
  • Accepted 31 July 2023
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