Ground State of the Asymmetric Anderson Model: Perturbation Approach with Respect to the s-d Mixing Integral

Abstract

The ground state of the asymmetric Anderson model is investigated in the limit of strong d-electron correlation. The secular equation for the ground state energy is expanded into the perturbation series with respect to s-d mixing integral, V, or the width of the d-level, Δ. When the energy level of the localized d-state is near the Fermi level, Ed≃0, it is shown that this secular equation is equivalent, up to the third dominant order, to the coupled integral equations for two self-energies Σ0(ω) and Σ1(ω) which are introduced for the d-unoccupied state and for the d-occupied state, respectively. The ground state energy and other physical quantities such as the d-electron number and spin- and charge-susceptibilities can be expressed in terms of Σ0 and Σ1. By solving the integral equations, these quantities are calculated numerically as a function of D and Δ, and also analytically in the limit of small values of Δ/D, D being the width of the conduction band.