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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.
Highlights
In thermodynamic equilibrium, a transition to a state with a spontaneous broken symmetry can be induced by a change in the external conditions or in the control parameters
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 energy
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
Summary
A transition to a state with a spontaneous broken symmetry can be induced by a change in the external conditions (such as temperature or pressure) or in the control parameters (such as an external applied field). The most widely studied examples are for systems at nonzero temperature, in the framework of classical phase transitions [1]. Equilibrium thermal fluctuations are responsible for the critical behavior associated with the discontinuous change of the thermodynamic properties of the system. Transitions may occur at zero temperature, as a function of some coupling constant [2]; in that case, since there are no thermal fluctuations, quantum fluctuations play a prominent role.
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