From the open Heisenberg model to the Landau-Lifshitz equation

Abstract

Magnetic systems can be described by the classical Landau-Lifshitz (LL) equation or the fully quantum open Heisenberg model. Using the Lindblad master equation and the mean-field approximation, we demonstrate that the open Heisenberg model is reduced to a generalized LL equation. The open dynamic is modeled using spin-boson interactions with a common bosonic reservoir at thermal equilibrium. By tracing out the bosonic degrees of freedom, we obtain two different decoherence mechanisms: on-site dissipation and an effective spin-spin interaction mediated by bosons. Using our approach, we perform hysteresis calculations, closely connected with the Stoner-Wohlfarth theory. We compare the exact numerical master equation and the mean-field model, revealing the role of correlations originated by non-local interactions. Our work opens new horizons for the study of the LL dynamics from an open quantum formalism.

11 pages, 6 figures

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• Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device
• Engineering non-Markovianity from defect-phonon interactions
• Landau-Lifshitz damping from Lindbladian dissipation in quantum magnets
• Unquenched orbital angular momentum as the origin of spin inertia
• Quantum fluctuation in rotation velocity of a levitated magnetic particle