Extremely correlated Fermi liquid study of theU=∞Anderson impurity model

Abstract

We apply the recently developed extremely correlated Fermi liquid (ECFL) theory to the Anderson impurity model, in the extreme correlation limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$. We develop an expansion in a parameter $\ensuremath{\lambda}$, related to ${n}_{d}$, the average occupation of the localized orbital, and find analytic expressions for the Green's functions to $O({\ensuremath{\lambda}}^{2})$. These yield the impurity spectral function and also the self-energy $\ensuremath{\Sigma}(\ensuremath{\omega})$ in terms of the two self-energies of the ECFL formalism. The imaginary parts of the latter have roughly symmetric low-energy behavior ($\ensuremath{\propto}{\ensuremath{\omega}}^{2}$), as predicted by Fermi liquid theory. However, the inferred impurity self-energy ${\ensuremath{\Sigma}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$ develops asymmetric corrections near ${n}_{d}\ensuremath{\rightarrow}1$, 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 overbroadening 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.