An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

TL;DR

This paper develops an advanced self-consistent approach to analyze the spectral properties of the Anderson impurity model, accurately capturing low-temperature behaviors and many-body effects beyond traditional approximations.

Contribution

It introduces a conserving approximation scheme that improves upon the NCA, accurately describing the impurity density of states and spin fluctuations at finite temperatures.

Findings

Accurately predicts the position and width of the Abrikosov-Suhl resonance.

Shows excellent agreement with Bethe-Ansatz results for magnetic susceptibility.

Provides detailed analysis of the resonant level and intermediate valence regimes.

Abstract

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.