The study of dissipative phase transitions is an emerging topic of research for quantum many-body systems out of equilibrium, which can be realized in artificial platforms using Rydberg atoms, semiconductor microstructures or superconducting circuits. In a dissipative phase transitions, the non-equilibrium steady state abruptly changes as a system parameter is varied, due to the competition between the coherent Hamiltonian dynamics and the dissipation processes.
Recently, unconventional magnetic phase transitions have been predicted in spin lattices described by a dissipative Heisenberg model with anisotropic spin-spin coupling and incoherent spin relaxation: in particular, the predictions have been based on single-site  and cluster mean-field  theory. A crucial problem is to explore the physical properties beyond mean-field.
By applying the corner-space renormalization method , we have explored the critical behavior of such class of spin systems . We have been able to investigate the finite-size scaling and to calculate the critical exponent of the magnetic linear susceptibility. We show that the Von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. At the same time, the quantum Fisher information, an entanglement witness, exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role. Our results suggest that dissipative phase transition can share properties of both thermal and quantum phase transitions.
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