Barnes slave boson approach to the two-site single impurity Anderson model with non-local interaction

TL;DR

This paper revisits the Barnes slave boson method for the two-site single impurity Anderson model with non-local interactions, providing exact calculations and comparing them to saddle-point approximations.

Contribution

It demonstrates the exact evaluation of path integrals in the model and compares these results to saddle-point approximations, highlighting their agreement in certain regimes.

Findings

Exact path integral evaluation for the model

Saddle-point approximation recovers exact results at strong non-local interaction

Good agreement between methods over a wide parameter range

Abstract

The Barnes slave boson approach to the $U=\infty$ single impurity Anderson model extended by a non-local Coulomb interaction is revisited. We demonstrate first that the radial gauge representation facilitates the treatment of such a non-local interaction by performing the \emph{exact} evaluation of the path integrals representing the partition function, the impurity hole density and the impurity hole density autocorrelation function for a two-site cluster. The free energy is also obtained on the same footing. Next, the exact results are compared to their approximations at saddle-point level, and it is shown that the saddle point evaluation recovers the exact answer in the limit of strong non-local Coulomb interaction, while the agreement between both schemes remains satisfactory in a large parameter range.