Failure of mean-field approach in out-of-equilibrium Anderson model

TL;DR

This paper investigates the limitations of the mean-field approximation in out-of-equilibrium Anderson models, revealing its failure to accurately predict magnetic states, local moments, and physical quantities under bias.

Contribution

It demonstrates the failure of the mean-field approach in out-of-equilibrium Anderson models, highlighting inaccuracies in predicting magnetic states and physical properties.

Findings

Mean field predicts stable magnetic and non-magnetic solutions in certain parameter regions.

Hysteresis observed in magnetization and current as bias varies.

Mean field fails to accurately predict local moments and introduces unphysical features.

Abstract

To explore the limitations of the mean field approximation, frequently used in \textit{ab initio} molecular electronics calculations, we study an out-of-equilibrium Anderson impurity model in a scattering formalism. We find regions in the parameter space where both magnetic and non-magnetic solutions are stable. We also observe a hysteresis in the non-equilibrium magnetization and current as a function of the applied bias voltage. The mean field method also predicts incorrectly local moment formation for large biases and a spin polarized current, and unphysical kinks appear in various physical quantities. The mean field approximation thus fails in every region where it predicts local moment formation.