Non-equilibrium properties of the S=1/2 Heisenberg model in a time-dependent magnetic field

TL;DR

This paper investigates the non-equilibrium dynamics of the S=1/2 Heisenberg model under a time-dependent magnetic field and phonon bath, revealing a threshold magnetic field below which magnetization fails to relax to equilibrium.

Contribution

It introduces a path integral approach to analyze the Heisenberg model with a phonon bath and identifies a minimal magnetic field necessary for magnetization relaxation.

Findings

Existence of a minimal magnetic field for relaxation

Qualitative agreement with mean field $\

Magnetization does not relax below this threshold

Abstract

The time-dependent behavior of the Heisenberg model in contact with a phonon heat bath and in an external time-dependent magnetic field is studied by means of a path integral approach. The action of the phonon heat bath is taken into account up to the second order in the coupling to the heath bath. It is shown that there is a minimal value of the magnetic field below which the average magnetization of the system does not relax to equilibrium when the external magnetic field is flipped. This result is in qualitative agreement with the mean field results obtained within $\phi^{4}$-theory.