Diagrammatic theory for Anderson Impurity Model. Stationary property of the thermodynamic potential

TL;DR

This paper develops a diagrammatic approach for the Anderson Impurity Model's normal state, incorporating generalized Wick's theorem and proving the stationarity of the thermodynamic potential with respect to correlation functions.

Contribution

It introduces a new diagrammatic method based on generalized Wick's theorem and establishes the stationary property of the thermodynamic potential in the Anderson Impurity Model.

Findings

Derived Dyson-like equations for Green's functions.

Expressed thermodynamic potential via renormalized Green's functions.

Proved stationarity of the thermodynamic potential with respect to correlation functions.

Abstract

A diagrammatic theory around atomic limit is proposed for normal state of Anderson Impurity Model. The new diagram method is based on the ordinary Wick's theorem for conduction electrons and a generalized Wick's theorem for gtrongly correlated impurity electrons. This last theorem coincides with the definition of Kubo cumulants. For the mean value of the evolution operator a linked cluster theorem is proved and a Dyson's type equations for one-particle propagators are established. The main element of these equations is the correlation function which contains the spin, charge and pairing fluctuations of the system. The thermodynamic potential of the system is expressed through one-particle renormalized Green's functions and the corelation function. The stationary property of the thermodynamic potential is established with respect to the changes of correlation function.