Limit cycle phase in driven-dissipative spin systems

TL;DR

This paper investigates the phase diagram of driven-dissipative spin-1/2 systems, revealing a limit cycle phase with oscillating magnetization, spatial fluctuations, and measurable spectral signatures, advancing understanding of non-equilibrium quantum phases.

Contribution

It introduces the existence of a limit cycle phase in driven-dissipative spin systems and analyzes its fluctuations and experimental signatures.

Findings

Discovery of a limit cycle phase with oscillating magnetization.

Spatial fluctuations induce quasi-long-range order in 2D.

Limit cycle phase shows an asymmetric power spectrum detectable experimentally.

Abstract

We explore the phase diagram of interacting spin-$1/2$ systems in the presence of anisotropic interactions, spontaneous decay and driving. We find a rich phase diagram featuring a limit cycle phase in which the magnetization oscillates in time. We analyze the spatio-temporal fluctuations of this limit cycle phase at the Gaussian level, and show that spatial fluctuations lead to quasi-long-range limit cycle ordering for dimension $d = 2$. This result can be interpreted in terms of a spatio-temporal Goldstone mode corresponding to phase fluctuations of the limit cycle. We also demonstrate that the limit-cycle phase exhibits an asymmetric power spectrum measurable in fluorescence experiments.