Dissipative Dynamics of an Interacting Spin System with Collective Damping 

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ABSTRACT

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-Keldysh technique, we derive mean field solution of the model and observe that the system breaks – 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 Ocorrection term which results change in various physically measurable quantities.

Significance of the study:

The research reveals the complex interplay between Hamiltonian and Lindblad dynamics in a long-range interacting spin system. By demonstrating z₂-symmetry breaking and deriving an effective temperature independent of dissipation rate and bath cutoff frequency, the study provides insights into non-equilibrium quantum phenomena. The findings, including modified dissipative spectra due to fluctuations, highlight the potential for novel physical behaviors in quantum systems, contributing to the understanding of driven-dissipative systems and their emergent thermal characteristics.

Summary of the study:

This study explores the dissipative dynamics in an infinite-range Heisenberg model coupled to a non-Markovian bath and subjected to Lindblad dynamics due to site-specific spin flipping. Using Holstein-Primakoff transformations and Schwinger-Keldysh technique, the system’s mean field solution shows z₂-symmetry breaking at the transition point. An effective temperature linearly dependent on system-bath coupling is derived, and fluctuations over the mean field are found to modify the dissipative spectrum with O(1/N) corrections.