In equilibrium physics, spontaneous symmetry breaking and elementary excitation are two concepts closely related with each other: the symmetry and its spontaneous breaking not only control the dynamics and spectrum of elementary excitations, but also determine their underlying structures. In this Letter, based on an exactly solvable model, we propose a phase ramping protocol to study an excitationlike behavior of a nonequilibrium quantum matter: a discrete time crystal phase with spontaneous temporal translational symmetry breaking. It is shown that slow ramping could induce a dynamical transition between two $Z_2$ symmetry breaking time crystal phases in time domain, which can be considered as a temporal analog of the soliton excitation spatially sandwiched by two degenerate charge density wave states in polyacetylene. By tuning the ramping rate, we observe a critical value at which point the transition duration diverges, resembling the critical slowing down phenomenon in nonequilibrium statistic physics. We also discuss the effect of stochastic sequences of such phase ramping processes and its implication to the stability of the discrete time crystal phase against noisy perturbations.

• Received 19 July 2020
• Revised 1 December 2020
• Accepted 23 December 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.020602