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

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 two-time auxiliary fields. After integration over the fermionic degrees of freedom, one obtains an effective action suitable for a 1/${\mathit{N}}_{\mathit{f}}$ expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and ${\mathit{N}}_{\mathit{f}}$\ensuremath{\rightarrow}\ensuremath{\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 spin-degenerate case ${\mathit{N}}_{\mathit{f}}$=2 the results are quite good.