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

To explore the limitations of the mean-field approximation, frequently used in 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 nonmagnetic solutions are stable. We also observe a hysteresis in the nonequilibrium 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.