Interplay between interference and Coulomb interaction in the ferromagnetic Anderson model with applied magnetic field

We study the competition between interference due to multiple single-particle paths and Coulomb interaction in a simple model of an Anderson-type impurity with local-magnetic-field-induced level splitting coupled to ferromagnetic leads. The model along with its potential experimental relevance in the field of spintronics serves as a nontrivial benchmark system where various quantum-transport approaches can be tested and compared. We present results for the linear conductance obtained by a spin-dependent implementation of the density-matrix renormalization-group scheme which are compared with a mean-field solution as well as a seemingly more advanced Hubbard-I approximation. We explain why mean field yields nearly perfect results while the more sophisticated Hubbard-I approach fails even at a purely conceptual level since it breaks hermiticity of the related density matrix. Furthermore, we study finite bias transport through the impurity by the mean-field approach and recently developed higher-order density-matrix equations. We found that the mean-field solution fails to describe the plausible results of the higher-order density-matrix approach both quantitatively and qualitatively, as it does not capture some essential features of the current-voltage characteristics such as negative differential conductance.