Dissipative quantum phase transition in an interacting many-particle system: from two-level to multilevel spins

The dissipative Lipkin-Meshkov-Glick model of N all-to-all interacting two-level systems subject to collective and/or individual decay is known to display a dissipative phase transition. There, the collective or individual nature of the dissipation defines the order of the phase transition and the characteristics of the different phases, while having no impact on the position of the critical point.
Here, we investigate a generalization of this model to d-level spins (d ≥ 2). While basic features of the transition, such as the critical point, remain identical to the two-level case, the spin expectation values that characterize the different phases become ever more distinct from each other as d increases. Furthermore, depending on the exact form of the dissipator, the critical point transforms into a critical region that grows with d. Around the phase transition, the steady state of the system is entangled, and different choices of the dissipator may lead to a suppression or even an enhancement of entanglement by the individual dissipation.