| Summary: | 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 Δ0. Simple second-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 behavior, Δ0Z/D≫1 and ≪1 (with Z the quasiparticle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ∑i(ω) is also examined beyond the confines of PT. It is argued that on frequency scales of order ω∼Δ0D, the self-energy in strong coupling is given precisely by the 2PT result, and we point out that the resultant poles in ∑i(ω) 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 behavior, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in U.
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