Non-interacting single-impurity Anderson model: solution without using the equation-of-motion method

TL;DR

This paper derives exact ground-state properties of the non-interacting symmetric single-impurity Anderson model using eigenenergy equations, providing explicit formulas and spectral functions that align with traditional methods.

Contribution

It offers a novel solution approach for the non-interacting SIAM without relying on the equation-of-motion method, including explicit formulas for key physical quantities.

Findings

Spectral functions match those from the equation-of-motion method

Impurity spectral function develops weight at band edges

Explicit formulas for ground-state energy and hybridization

Abstract

Ground-state properties of the non-interacting symmetric single-impurity Anderson model (SIAM) are derived from the corresponding eigenenergy equation. Explicit formulae are given for the ground-state energy, the hybridization, and the momentum distribution that are essential quantities for variational approaches to the interacting model. Various spectral functions, e.g., the total density of states, the phase shift function, and the impurity spectral function, are shown to agree with those obtained from the equation-of-motion method (see supplementary material). For a constant hybridization strength and a semi-elliptic host density of states it is seen that the impurity spectral function builds up weight at the band edges.