Asymptotically exact mean field theory for the Anderson model including double occupancy

TL;DR

This paper develops an asymptotically exact mean field theory for the Anderson impurity model that includes double occupancy effects, using a slave boson approach and path integral techniques to improve upon traditional methods.

Contribution

It introduces a novel approach combining slave boson representation and path integrals to accurately analyze the Anderson model with finite Coulomb repulsion, including double occupancy.

Findings

Exact ground state properties recovered at zero temperature and large N_f.

Numerical solutions show good accuracy even for N_f=2.

Method overcomes limitations of naive mean field theories.

Abstract

The Anderson impurity model for finite values of the Coulomb repulsion $U$ is studied using a slave boson representation for the empty and doubly occupied $f$-level. In order to avoid well known problems with a naive mean field theory for the boson fields, we use the coherent state path integral representation to first integrate out the double occupancy slave bosons. The resulting effective action is linearized using {\bf two-time} auxiliary fields. After integration over the fermionic degrees of freedom one obtains an effective action suitable for a $1/N_f$-expansion. Concerning the constraint the same problem remains as in the infinite $U$ case. For $T \rightarrow 0$ and $N_f \rightarrow \infty$ exact results for the ground state properties are recovered in the saddle point approximation. Numerical solutions of the saddle point equations show that even in the spindegenerate case $N_f = 2$ the results are quite good.