Excitation Spectra of the Two Impurity Anderson Model. I. Critical Transition in the Two Magnetic Impurity Problem and the Roles of the Parity Splitting

Excitation spectra of the two impurity Anderson model are calculated by using the numerical renormalization group method. The critical transition found by Jones et al. is examined based on the model that the parity splitting is induced by the f-f transfer matrix, t. The low energy scale, ω1/TK, is approximately given as ((j-jc)/1.5)2 + (t/23TK)2, and thus t suppresses the critical transition, where y is the exchange coupling normalized by the Kondo temperature TK, jc the critical value for the model without t. The γ-coefficient is proportional to ω1-1, while the antiferromagnetic susceptibility to In ωl-1. The phase shift changes continuously nearyc. It tends to singular jump as t→0. The parity splitting of the single particle excitation spectrum is enhanced by the exchange coupling.