Spectral properties of a narrow-band Anderson model

Abstract

We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth $D$ is small compared to the hybridization strength ${\Delta }_0$. Simple 2nd order perturbation theory (2PT) in $U$ is found to produce a rich spectral structure, that leads to rather good agreement with extant Lanczos results and offers a transparent picture of the underlying physics. It also leads naturally to two distinct regimes of spectral behaviour, ${\Delta }_{0}Z/D\gg 1$ and $\ll 1$ (with $Z$ the quasi-particle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ${\Sigma }_{i\omega }$ is also examined beyond the confines of PT. It is argued that on frequency scales of order $\omega \sim \sqrt{Delt{a}_{0}D}$, the self-energy in {\em strong} coupling is given precisely by the 2PT result, and we point out that the resultant poles in ${\Sigma }_{i\omega }$ connect continuously to that characteristic of the atomic limit. This in turn offers a natural rationale for the known inability of the skeleton expansion to capture such behaviour, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in $U$.

10 pages, 2 Postscript figures, uses RevTex 3.1; accepted for publication in Phys. Rev. B15

References in corpus (3)

• Density of states near the Mott-Hubbard transition in the limit of large dimensions
• Symmetric Anderson impurity model with a narrow band
• Renormalized vs unrenormalized perturbation-theoretical approaches to the Mott transition

Cited by in corpus (2)

• NRG for the bosonic single-impurity Anderson model: Dynamics
• The Anderson impurity model with a narrow-band host: from orbital physics to the Kondo effect