Infrared Divergence in Pseudo-Particle Spectra

Abstract

Infrared divergence in the pseudo-particle spectra of the degenerate impurity Anderson model described in terms of the auxiliary particles is examined rigorously with use of the expansion from the large limit of the spin-orbital degeneracy N . The results of analysis with the most divergent terms in the expansion confirm the exponents of the spectra of the slave boson and the pseudo-fermion to be given respectively by 1- n f 2 / N and (2 n f - n f 2 )/ N where n f is the average number of localized electrons at the impurity site, rather than by N /( N +1) and 1/( N +1) as suggested by the results of so-called non-crossing approximation (NCA) studies. In determination of the correct exponents, contributions from the crossing diagrams are crucial. It is also confirmed that all of the infrared divergences in the single particle spectra are cancelled out by the corresponding vertex corrections to leave only non-divergent terms in the scattering rate of the conduction electrons.