From Canonical to Tunable Phase Diagrams in Open Quantum Long-Range Systems

Abstract

We investigate the dissipative dynamics of a generalized Lipkin-Meshkov-Glick (LMG) model coupled to a thermal environment. In this generalized model, in addition to the conventional quadratic interaction, one considers quartic interactions between spin-$1/2$'s coupled all-to-all and evolving in presence of a transverse field. Employing the usual linear Lindblad master equation with thermally-balanced jump processes, we derive magnetisation evolution equations, and demonstrate that the corresponding stationary solution reproduces the canonical equilibrium phase diagram of the model. We then extend our analysis to a nonlinear Lindblad equation that incorporates imperfect quantum-jump processes in terms of jump-retention parameters. Here, remarkably, the system relaxes to a genuine nonequilibrium stationary state whose properties differ qualitatively from those obtained in the linear case. The jump-retention parameters provide tunable knobs that shift the phase boundaries and even modify the nature of the phase transitions with respect to the linear case. Our exact results establish a direct connection between dissipative relaxation dynamics and stationary-state behavior, while identifying controlled quantum-jump retention as a mechanism for engineering nonequilibrium phases in long-range interacting open quantum systems.