The competition between Hamiltonian and Lindblad dynamics in quantum systems give rise to non-equilibrium phenomena with no counterpart in conventional condensed matter physics. In this paper, we investigate this interplay of dynamics in infinite range Heisenberg model coupled to a non-Markovian bath and subjected to Lindblad dynamics due to spin flipping at a given site. The spin model is bosonized via Holestien-Primakoff transformations and is shown to be valid for narrow range of parameters in the thermodynamic limit. Using Schwinger-Keldyshtechnique, we derive mean field solution of the model and observe that the system breaks z2 - symmetry at the transition point. We calculate effective temperature that has linear dependence on the effective system-bath coupling, and is independent of the dissipation rate and cutoff frequency of the bath spectral density. Furthermore, we study the fluctuations over mean field and show that the dissipative spectrum is modified by O(1/N) correction term which results change in various physically measurable quantities.
Dar et al. (Fri,) studied this question.
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