Wick's Theorem and a New Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems

Abstract

A new type of perturbation expansion in the mixing $V$ of localized orbitals with a conduction-electron band in the $U\to\infty$ Anderson model is presented. It is built on Feynman diagrams obeying standard rules. The local correlations of the unperturbed system (the atomic limit) are included exactly, no auxiliary particles are introduced. As a test, an infinite-order ladder-type resummation is analytically treated in the Kondo regime, recovering the correct energy scale. An extension to the Anderson-lattice model is obtained via an effective-site approximation through a cumulant expansion in $V$ on the lattice. Relation to treatments in infinite spatial dimensions are indicated.