Extremely Correlated Fermi Liquid study of the U=infinity Anderson Impurity Model

TL;DR

This paper applies the extremely correlated Fermi liquid theory to the Anderson impurity model at extreme correlation, deriving analytic Green's functions and analyzing spectral functions, with results consistent with known numerical methods.

Contribution

It develops an analytic expansion in a correlation parameter for the Anderson impurity model within the ECFL framework, providing new insights into spectral functions and self-energies.

Findings

Impurity spectral function becomes asymmetric near n_d ~ 1

Friedel sum rule is satisfied within approximation

Spectrum agrees with NRG results after frequency scaling

Abstract

We apply the recently developed extremely correlated Fermi liquid theory to the Anderson impurity model, in the extreme correlation limit. We develop an expansion in a parameter \lambda, related to n_d, the average occupation of the localized orbital, and find analytic expressions for the Green's functions to O(\lambda^2). These yield the impurity spectral function and also the self-energy \Sigma(\omega) in terms of the two self energies of the ECFL formalism. The imaginary parts of the latter, have roughly symmetric low energy behaviour (~ \omega^2), as predicted by Fermi Liquid theory. However, the inferred impurity self energy \Sigma"(\omega) develops asymmetric corrections near n_d ~ 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an over broadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.