Exact solution of the Anderson model: I

Abstract

The complete solution of the non-degenerate Anderson model describing the formation of the localised moment in a metal is constructed on the basis of the Bethe ansatz method. Explicit expressions for the magnetic susceptibility and specific heat are derived at zero temperature but with arbitrary parameters U, Gamma and epsilon _d. In the symmetric case the dependence of the impurity magnetisation on the magnetic field is obtained at zero temperature. The asymmetric Anderson model is studied in detail. Explicit expressions for the dependence of the susceptibility and occupation number on the effective resonance level position are derived.