Dissipative prethermal discrete time crystal

TL;DR

This paper investigates how dissipation affects the lifetime of prethermal discrete time crystals, revealing a non-monotonic relationship where moderate dissipation can prolong or shorten their stability.

Contribution

It provides a theoretical analysis of dissipation's dual role in extending or destabilizing prethermal DTCs, highlighting the non-monotonic effects of environment coupling.

Findings

Dissipation can extend the prethermal period by slowing error accumulation.

Strong environment coupling destabilizes spontaneous symmetry breaking.

Prethermal DTC survival time varies non-monotonically with dissipation strength.

Abstract

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 sub-harmonic 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 non-monotonic variation, i.e. the survival time of the prethermal DTC first increases and then decreases as the environment coupling gets stronger.