Symmetric Anderson impurity model with a narrow band

TL;DR

This paper investigates the symmetric Anderson impurity model in the narrow band limit, revealing a negative impurity density of states contribution, a new thermodynamic crossover, and the breakdown of skeleton expansion, while confirming Luttinger's theorem.

Contribution

It introduces analysis of the narrow band limit in the symmetric Anderson model, highlighting new effects on density of states and spectral functions, and examines the validity of Fermi liquid properties.

Findings

Impurity contribution to density of states is negative in narrow band systems.

A new crossover in thermodynamic quantities is identified.

Skeleton expansion breaks down at intermediate energies, but Luttinger's theorem remains valid.

Abstract

The single channel Anderson impurity model is a standard model for the description of magnetic impurities in metallic systems. Usually, the bandwidth represents the largest energy scale of the problem. In this paper, we analyze the limit of a narrow band, which is relevant for the Mott-Hubbard transition in infinite dimensions. For the symmetric model we discuss two different effects: i) The impurity contribution to the density of states at the Fermi surface always turns out to be negative in such systems. This leads to a new crossover in the thermodynamic quantities that we investigate using the numerical renormalization group. ii) Using the Lanczos method, we calculate the impurity spectral function and demonstrate the breakdown of the skeleton expansion on an intermediate energy scale. Luttinger's theorem, as an example of the local Fermi liquid property of the model, is shown to still be valid.