Stability of emergent time periodicity in a few-body interacting system

TL;DR

This paper investigates how emergent time periodicity in a few-body Lipkin-Meshkov-Glick model is affected by thermal baths and internal interactions, revealing conditions for stability and the impact of temperature.

Contribution

It demonstrates that stable time-periodic behavior requires a purely dissipative bath and compares effects of temperature on different interaction types.

Findings

Time periodicity is stable only with a purely dissipative bath.

Temperature destroys time periodicity in all-to-all interactions.

Nearest neighbor interactions maintain long-time periodic behavior despite temperature.

Abstract

We examine the onset and resilience of emergent time periodicity in a few-body all-to-all interacting Lipkin-Meshkov-Glick model, where one of the constituents is locally in contact with a thermal bath. Employing both a collision model framework and a suitable time-continuous description, we show that stable time-periodic behavior can only be exhibited when the bath acts as a purely dissipative channel. We assess the role that the microscopic interactions within the system play, establishing that for the all-to-all model the introduction of temperature leads to a melting of the emergent time periodicity, in contrast to stable long-time behavior which can be maintained for nearest neighbor $XXZ$ type interactions.