Solvable model for discrete time crystal enforced by nonsymmorphic dynamical symmetry

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.