From the open generalized 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 generalized Heisenberg model. Using the Lindblad master equation and the mean-field approximation, we demonstrate that the open generalized 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.

Keywords

• open Heisenberg model
• spin dynamics
• open quantum systems
• Landau–Lifshitz equation