The Finite-$U$ Impurity Anderson Model in the presence of an external magnetic field

TL;DR

This paper studies how an external magnetic field affects the finite-U impurity Anderson model, revealing that the Kondo temperature decreases and exhibits scaling behavior, with implications for impurity magnetization at finite temperatures.

Contribution

It introduces two computationally efficient approximations for the vertex function in the slave boson approach, enabling detailed analysis of magnetic field effects in the finite-U Anderson model.

Findings

Kondo temperature is reduced by magnetic field.

Field dependence of Kondo temperature and magnetization shows scaling behavior.

Finite temperature magnetization features are explained via renormalized Kondo temperature.

Abstract

We have investigated effects of an external magnetic field in the impurity Anderson model with a finite on-site Coulomb repulsion $U$. Large $N_f$ expansion is employed in the slave boson representation, by taking into account $f^0$, $f^1$, and $f^2$ subspaces. To evaluate the vertex function for the ``empty state boson" self-energy, we have devised two approximations which reduce much computational efforts without losing general features of the model. It is found that the Kondo temperature is reduced by the presence of a magnetic field, and that at low field and at low temperature, the field dependence of both the Kondo temperature and the impurity magnetization exhibits a scaling behavior with high accuracy. Further, some interesting features are found in the field dependence of the impurity magnetization at finite temperature, the physical implications of which are discussed in terms of the renormalized Kondo temperature.