A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry*

Discrete time crystal is a class of non-equilibrium quantum systems that exhibits subharmonic response to periodic driven. In this paper, we propose a kind of discrete time crystal enforced by nonsymmorphic dynamical symmetry. When a system hosts certain nonsymmorphic dynamical symmetry, the symmetry will enforce the instantaneous states Mobius twisted and double the period of the instantaneous state. When the evolution speed of the system equals proper parameters, or the system is in the long-period limit, it will spontaneously exhibit a period expansion without undergoing quantum superposition states. The system also hosts a half-integer topological invariance and a pi Berry phase after two periods of evolution.