Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems

TL;DR

This paper demonstrates that short-range correlations significantly alter the steady-state phase diagram of dissipative quantum spin systems, revealing new phases and reentrant behavior through an advanced cluster mean-field approach.

Contribution

It introduces a novel cluster mean-field method combining equilibrium and nonequilibrium techniques to analyze dissipative many-body quantum systems.

Findings

Short-range correlations change phase boundaries and topology.

Reentrant paramagnetic phase appears in the phase diagram.

Potential incommensurate ordering instability identified.

Abstract

We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1=2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.