Non-equilibrium magnetic phases in spin lattices with gain and loss

We study the magnetic phases of a nonequilibrium spin chain, where coherent interactions between neigh-boring lattice sites compete with alternating gain and loss processes. This competition between coherent and incoherent dynamics induces transitions between magnetically aligned and highly mixed phases, across which the system changes from a low to an infinite temperature state. We show that the origin of these transitions can be traced back to the dynamical effect of parity-time-reversal symmetry breaking, which has no counterpart in the theory of equilibrium phase transitions. This mechanism also results in very atypical features and we find first-order transitions without phase coexistence and mixed-order transitions which do not break the underlying U(1) symmetry, even in the appropriate thermodynamic limit. Thus, despite its simplicity, the current model considerably extends the phenomenology of nonequilibrium phase transitions beyond that commonly assumed for driven-dissipative spins and related systems.