Non-equilibrium itinerant-electron magnetism: a time-dependent mean-field theory

TL;DR

This paper develops a theoretical framework to analyze the dynamical magnetic response of strongly correlated electrons out of equilibrium, providing new definitions for magnon frequencies and exchange parameters in time-dependent settings.

Contribution

It introduces a generalized Bethe-Salpeter equation for non-equilibrium systems and derives explicit expressions for magnetic susceptibilities and exchange parameters.

Findings

Derived a non-equilibrium transverse magnetic susceptibility expression.

Provided a rigorous definition of non-equilibrium magnon frequencies.

Recovered known equilibrium results as a special case.

Abstract

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the non-equilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of non-equilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of non-equilibrium single-electron Green functions and self-energies. In the particular case of equilibrium, we recover previously known results.