Diagrammatic Approach to the Anderson Model for Dilute Alloys

Applications of a new diagrammatic technique for the grand partition function Z and the susceptibility of the Anderson Hamiltonian are presented, where the hopping is treated as a perturbation. Z is expressed quite generally in terms of statistical quasiparticles. For -εd>W (bandwidth) and for U→∞ for simplicity, this formulation allows one to show that the thermodynamics of the Anderson model and of an s-d model with an effective J (essentially in agreement, but slightly renormalized compared to the one obtained from the Schrieffer-Wolff transformation) are equivalent. Indication is given that this equivalence is more complicated for the dynamical properties of the model, as reflected, e.g., by the scattering matrix.