Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model

TL;DR

This paper introduces a new, more accurate method for calculating the self-energy in the impurity Anderson model using the Numerical Renormalization Group, with implications for understanding the metal-insulator transition.

Contribution

A novel approach to compute the self-energy directly as a ratio of correlation functions within NRG, improving reliability over traditional methods.

Findings

More accurate self-energy calculations demonstrated.

Application to constant coupling and DMFT scenarios.

Implications for metal-insulator transition analysis.

Abstract

We present a new method to calculate directly the one-particle self-energy of an impurity Anderson model with Wilson's numerical Renormalization Group method by writing this quantity as the ratio of two correlation functions. This way of calculating Sigma(z) turns out to be considerably more reliable and accurate than via the impurity Green's function alone. We show results for the self-energy for the case of a constant coupling between impurity and conduction band (ImDelta = const) and the effective Delta(z) arising in the Dynamical Mean Field Theory of the Hubbard model. Implications to the problem of the metal-insulator transition in the Hubbard model are also discussed.