Green's Functions for the Anderson model: the Atomic Approximation

TL;DR

This paper develops an approximation method for calculating Green's functions in the periodic Anderson model, extending previous work to finite U and providing explicit formulas applicable to both PAM and SIAM.

Contribution

The paper introduces the Atomic Approximation for the cumulant expansion of the PAM, extending it to finite U and deriving explicit Green's function expressions for PAM and SIAM.

Findings

Provides formal exact Green's functions with effective cumulants.

Extends the Atomic Approximation to finite U cases.

Offers explicit formulas for Green's functions in PAM and SIAM.

Abstract

We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as difficult to calculate as the original GF, and the Atomic Approximation consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. This approximation has already been used for the case of infinite electronic repulsion U (Phys. Rev. B 62, 7882 (2000)), and here we extend the treatment to the case of finite U. The method can also be applied to the single impurity Anderson model (SIAM), and we give explicit expressions of the approximate GF both for the PAM and the SIAM.