Emergence and stability of discrete time-crystalline phases in open quantum systems

TL;DR

This paper develops a theoretical framework to analyze the emergence and stability of discrete time-crystalline phases in open quantum many-body systems, emphasizing the role of dissipation, fluctuations, and temperature effects.

Contribution

It introduces a fluctuation-regulated quantum master equation to study DTC phases, highlighting how dissipators and thermal fluctuations influence their robustness and stability.

Findings

Longer fluctuation correlation times enhance DTC stability.

DTC robustness is directly linked to dissipative effects from drive and dipolar interactions.

Temperature increases degrade DTC performance.

Abstract

Here we provide a theoretical framework to analyze discrete time-crystalline phases (DTC) in open quantum many-body systems. As a particular realization, we choose a quantum many-body system that exhibits cascaded prethermalization . The analysis uses a fluctuation-regulated quantum master equation. The master equation captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the dissipators from the drive and the dipolar interactions lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. Our results are in good agreement with the experiments. Finally, we show and quantify how the DTC performance degrades with temperature.