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

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Jiasen Jin, Alberto Biella, Oscar Viyuela, Leonardo Mazza, Jonathan Keeling, Rosario Fazio, and Davide Rossini



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 time, whereas in thermodynamic equilibrium it arises from the properties of the (free-)energy. Tiny correlations may be amplified in the dynamics and therefore have a strong impact in the steady state. To this scope, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to non-equilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spins-1/2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment which 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 re-entrance 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.