PT-symmetry breaking phase transitions in an LMG dimer

The open Lipkin-Meshkov-Glick (LMG) model provides a prototype of a dissipative phase transition which can be analyzed using mean-field theory. By combining the physics of this model with those of a quantum analogue of a parity-time reversal symmetry breaking transition we analyze the steady states phase diagram of a pair of coupled LMG models. The interplay of these two distinct physical effects leads to a complex phase diagram with multiple different types of steady state. We show that the effects predicted from mean-field theory survive in the full quantum model.