Numerical Renormalization Group Study of Pseudo-Fermion and Slave-Boson Spectral Functions in the Single Impurity Anderson Model

TL;DR

This paper employs the numerical renormalization group to analyze auxiliary spectral functions in the infinite-U Anderson impurity model, revealing threshold divergences and impurity occupation dependence of exponents.

Contribution

It provides the first NRG-based calculation of the exponents for auxiliary spectral functions in the U=∞ Anderson model, highlighting the importance of vertex corrections.

Findings

Spectral functions diverge at the threshold with exponents related to conduction electron phase shifts.

Exact exponents depend on impurity occupation number, differing from NCA results.

Vertex corrections are singular at the threshold and significant in the Fermi liquid regime.

Abstract

We use the numerical renormalization group to calculate the auxiliary spectral functions of the $U=\infty$ Anderson impurity model. The slave--boson and pseudo--fermion spectral functions diverge at the threshold with exponents $\alpha_{b}$ and $\alpha_{f}$ given in terms of the conduction electron phase shifts by the X--ray photoemission and the X--ray absorption exponents respectively. The exact exponents obtained here depend on the impurity occupation number, in contrast to the NCA results. Vertex corrections in the convolution formulae for physical Green's functions are singular at the threshold and may not be neglected in the Fermi liquid regime.