An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

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.

19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof/

References in corpus (3)

• Transport Coefficients of the Anderson Model via the Numerical Renormalization Group
• Numerical Renormalization Group Study of Pseudo-Fermion and Slave-Boson Spectral Functions in the Single Impurity Anderson Model
• Perturbational Approach to the Anderson Model: New Results from a Post-Nca Treatment

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• Renormalization Group Approach to Spectral Properties of the Two-Channel Anderson Impurity Model
• Effects of vertex corrections on diagrammatic approximations applied to the study of transport through a quantum dot
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Diagrammatic method for investigating universal behavior of impurity systems
• Quantitative comparison of Anderson impurity solvers applied to transport in quantum dots
• Dynamic susceptibilities of the single impurity Anderson model within an enhanced non-crossing approximation
• Self-Consistent Strong-Coupling-Perturbation Theory for the Anderson Model, Based on Wicks Theorem