Dissipation Mechanisms and Dissipative Phase Transitions of two coupled Fully Connected Quantum Ising models

TL;DR

This paper investigates how different dissipative mechanisms influence phase transitions in coupled quantum Ising models, revealing both equilibrium-like and nonequilibrium critical behaviors.

Contribution

It introduces a detailed analysis of two classes of dissipators and their impact on the nature of dissipative phase transitions in coupled quantum Ising systems.

Findings

Relaxation dynamics depend on the quench protocol and dissipator type.

Steady states can resemble thermal Gibbs states or be genuinely nonequilibrium.

Strong coupling can lead to reentrant phases with multiple phase transitions.

Abstract

We study dissipative phase transitions in a system of two coupled fully-connected quantum Ising models interacting with an environment. The dynamics is governed by a Lindblad master equation combining coherent unitary evolution and incoherent dissipative processes, where the unitary part is described within a self-consistent mean-field framework effectively acting on the local Hilbert space of two coupled spins at each site. We analyze two fundamentally different classes of dissipators. In the first case, the jump operators are defined in the instantaneous eigenbasis of the mean-field Hamiltonian and satisfy a detailed-balance condition. In this setting, the relaxation dynamics depends strongly on the quench protocol: a parametric quench of the Hamiltonian leads to conventional relaxation, whereas a temperature quench gives rise to a dynamical phase transition characterized by nonanalytic behavior in time. Yet, in both cases, the system relaxes toward a steady state determined solely by the post-quench parameters and the bath temperature, which closely resembles a thermal Gibbs state of the mean-field Hamiltonian. As a result, the dissipative phase transition occurs at a critical point consistent with the corresponding equilibrium transition. In contrast, when the dissipators are realized via local spin raising and lowering operators, the steady state is genuinely nonequilibrium, leading to a significantly richer phase diagram. In particular, for sufficiently strong system-bath coupling, we observe a reentrant phase featuring a symmetry-broken region bounded by two continuous dissipative phase transitions. Our results evidence how the structure of dissipative processes controls the emergence of equilibrium-like versus genuinely nonequilibrium critical behavior in open quantum systems.