Thermal melting of discrete time crystals: A dynamical phase transition induced by thermal fluctuations

The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically driven classical system composed of interacting spins, each of which couples to a thermal bath. It is shown that in the thermodynamic limit, even though the long-range temporal crystalline order is stable at low temperature, it is melting above a critical temperature, at which the system experiences a nonequilibrium phase transition. The critical behaviors of the continuous phase transition have been systematically investigated, and it is shown that despite the genuine nonequilibrium feature of such a periodically driven system, its critical properties fall into the three-dimensional Ising universality class with a dynamical exponent (z = 2) identical to that in the critical dynamics of a kinetic Ising model without driving.

Automated summary

This study numerically investigates the stability of a discrete time crystal against thermal fluctuations. It reveals that while the long-range temporal crystalline order is stable at low temperature, it melts and undergoes a non-equilibrium phase transition above a critical temperature. The critical properties of the continuous phase transition are systematically studied and found to fall into the same universality class as the kinetic Ising model without driving, despite the genuine nonequilibrium feature of the periodically driven system.