Interpolative Approach for Solving the Anderson Impurity Model

TL;DR

This paper introduces an interpolative method for solving the Anderson impurity model using a rational self-energy representation, constrained by physical sum rules and validated against quantum Monte Carlo results.

Contribution

It develops a new interpolation approach for the Anderson impurity model's self-energy, combining analytical constraints with fast approximation techniques.

Findings

Spectral functions agree with quantum Monte Carlo results.

The method accurately captures the effects of doping and interaction strength.

Provides a computationally efficient alternative to exact methods.

Abstract

A rational representation for the self--energy is explored to interpolate the solution of the Anderson impurity model in general orbitally degenerate case. Several constrains such as the Friedel's sum rule, positions of the Hubbard bands as well as the value of quasiparticle residue are used to establish the equations for the coefficients of the interpolation. We employ two fast techniques, the slave--boson mean--field and the Hubbard I approximations to determine the functional dependence of the coefficients on doping, degeneracy and the strength of the interaction. The obtained spectral functions and self--energies are in good agreement with the results of numerically exact quantum Monte Carlo method.