Limit-cycle phase in driven-dissipative spin systems

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 spatiotemporal fluctuations of this limit-cycle phase based on a Gaussian-Floquet analysis. Spatial fluctuations destroy long-range limit-cycle ordering for dimension d <= 2, as a time-dependent generalization of the Mermin-Wagner theorem. This result can be interpreted in terms of a spatiotemporal 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.