Prethermal discrete time crystals (PDTCs), an emergent nonequilibrium phase of matter, have been studied in two- and higher-dimensional lattices with nearest-neighbor (NN) interactions and one-dimensional (1D) lattices with long-range interactions. However, different from prethermalization that can be observed in 1D Floquet classical spin systems with NN interactions, classical PDTCs in Floquet 1D systems with only NN interactions have not been proposed before. Here, we demonstrate the emergence of disorder-free discrete time crystals (DTCs) in 1D Floquet classical spin systems with NN interactions. We show that the thermalization time first grows exponentially as the driving frequency increases and is then saturated, which depends on the energy density of the initial state. Since thermalization of the effective Hamiltonian is slow, there is no typical prethermalization and PDTCs in the Floquet system before final thermalization. The robustness of DTC order is verified by introducing imperfect spin flip operations. Our work provides an exploration of quantum characteristics, when considering the classical counterparts of quantum phenomena, and will be helpful for further investigations of both classical and quantum prethermal systems and discrete time-crystalline order.
Discrete time crystals (DTCs) are phases of matter characterized by the presence of an observable evolving with
nT periodicity under a
T-periodic Hamiltonian, where
n>1 is an integer insensitive to small parameter variations. In particular, DTCs with
n=2 have been extensively studied in periodically quenched and kicked spin systems in recent years. In this paper, we study the emergence of DTCs in a many-body system whose semiclassical mean-field dynamics is nonintegrable, using a rather simple model depicting a harmonically driven spin chain. We advocate to first employ a semiclassical approximation to arrive at a mean-field Hamiltonian and then identify the parameter regime at which DTCs exist, with standard tools borrowed from studies of classical chaos. Specifically, we seek symmetric-breaking solutions by examining the stable islands on the Poincar\'e surface of section of the mean-field Hamiltonian. We then turn to the actual many-body quantum system, evaluate the stroboscopic dynamics of the total magnetization in the full quantum limit, and verify the existence of DTCs. Our effective and straightforward approach indicates that in general DTCs are one natural aspect of many-body quantum chaos with mixed classical phase space structure. Our approach can also be applied to general time-periodic systems, which is thus promising for finding DTCs with
n>2 and opening possibilities for exploring DTCs properties beyond their time-translational breaking features.
Prethermal discrete time crystals (pDTC) are new collective nonequilibrium phases of matter that break, up to exponentially long times, the discrete time translational symmetry of a periodic drive. Previously studied as a quantum phenomenon, this paper establishes that pDTCs also emerge for classical Hamiltonian dynamics even in their `higher-order and fractional' version. This enables efficient simulations of such phenomena in experimentally relevant settings, including a study of the interplay between dimensionality and interaction range.