Dissipative Prethermal Discrete Time Crystal

An ergodic system subjected to an external periodic drive will be generically heated to infinite temperature. However, if the applied frequency is larger than the typical energy scale of the local Hamiltonian, this heating stops during a prethermal period that extends exponentially with the frequency. During this prethermal period, the system may manifest an emergent symmetry that, if spontaneously broken, will produce subharmonic oscillation of the discrete time crystal (DTC). We study the role of dissipation on the survival time of the prethermal DTC. On one hand, a bath coupling increases the prethermal period by slowing down the accumulation of errors that eventually destroy prethermalization. On the other hand, the spontaneous symmetry breaking is destabilized by interaction with environment. The result of this competition is a nonmonotonic variation, i.e., the survival time of the prethermal DTC first increases and then decreases as the environment coupling gets stronger.

Automated summary

An ergodic system subjected to an external periodic drive will be heated to infinite temperature, but this heating can be stopped during a prethermal period if the applied frequency is larger than the typical energy scale of the local Hamiltonian. This prethermal period exhibits an emergent symmetry that, if broken, leads to subharmonic oscillation of the discrete time crystal (DTC). The presence of dissipation affects the survival time of the prethermal DTC, with a bath coupling prolonging the prethermal period and interaction with the environment destabilizing spontaneous symmetry breaking, resulting in a nonmonotonic variation of the survival time.