From the open Heisenberg model to the Landau-Lifshitz equation

TL;DR

This paper derives a generalized Landau-Lifshitz equation from the open quantum Heisenberg model using Lindblad dynamics, revealing decoherence mechanisms and enabling hysteresis analysis.

Contribution

It introduces a method to connect the quantum open Heisenberg model with the classical LL equation via mean-field approximation and spin-boson interactions.

Findings

Decoherence mechanisms include on-site dissipation and boson-mediated spin interactions.

Comparison between exact and mean-field models highlights the role of correlations.

Hysteresis calculations demonstrate the model's applicability to magnetic phenomena.

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.