A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models

TL;DR

This paper introduces a new numerical renormalization group method for calculating dynamical correlation functions in quantum impurity models, ensuring accurate spectral sum rules and thermodynamic quantities.

Contribution

It develops a complete basis set approach that avoids overcounting and improves the accuracy of Green's function calculations in equilibrium impurity systems.

Findings

Accurately reproduces spectral sum rules.

Consistently matches thermodynamic expectation values.

Eliminates overcounting of excitations.

Abstract

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values, such as occupancy and magnetization, obtained directly from the numerical renormalization group calculations.