Diagrammatic approach for Impurity Anderson Model

Abstract

Impurity Anderson Model is the model for a system of conduction electrons that interact with a local spin as just another electrons in f – orbitals. The Hamiltonian of the system contains hybridization interaction between band electrons and localized electrons. The Coulomb interaction of two localized electrons is far too large to be treated by perturbation theory and it must be included in non interacting part of the Hamiltonian. Including this term invalidates Wick theorem for local electrons and makes problems in doing the Green’s function expansion. It is propose a new approach to solving the Anderson model and as a new Wick theorem is used the definition of the Kubo cumulants of impurity electrons, named as irreducible Green’s functions. For conduction electron subsystem the ordinary Wick theorem is available. The thermodynamic perturbation theory for Matsubara Green’s functions has been elaborated considering the hybridization term of the Hamiltonian as a perturbation one of two subsystems of independent conduction and impurity electrons.