Quantum correlations in the one-dimensional driven dissipative XY model

We study the nonequilibrium steady state (NESS) of a driven dissipative one-dimensional system near a critical point, and explore how the quantum correlations compare to the known critical behavior in the ground state. The model we study corresponds to a cavity array driven parametrically at a two photon resonance, equivalent in a rotating frame to a transverse field anisotropic XY model [C.-E. Bardyn and A. Imamoglu, Phys. Rev. Lett. 109, 253606 (2012)]. Depending on the sign of transverse field, the steady state of the open system can be either related to the ground state or to the maximum energy state. In both cases, many properties of the entanglement are similar to the ground state, although no critical behavior occurs. As one varies from the Ising limit to the isotropic XY limit, entanglement range grows. The isotropic limit of the NESS is, however, singular, with simultaneously diverging range and vanishing magnitude of entanglement. This singular limiting behavior is quite distinct from the ground state behavior; it can, however, be understood analytically within spin-wave theory.