Open Wilson chain numerical renormalization group approach to Green's functions

TL;DR

This paper introduces an open Wilson chain method combining NRG with a Bloch-Redfield approach to accurately compute impurity spectral functions without artificial broadening, improving spectral resolution.

Contribution

It presents a novel open Wilson chain framework that reproduces the continuous coupling function and naturally broadens spectral functions using a combined NRG and Bloch-Redfield approach.

Findings

Eliminates artificial broadening in spectral functions.

Achieves accurate spectral representation in magnetic fields.

Provides a natural broadening mechanism via finite lifetimes.

Abstract

By combining Wilson's numerical renormalization group with a modified Bloch-Redfield approach we are able to eliminate the artificial broadening of the Lehmann representation of quantum impurity spectral functions required by the standard numerical renormalization group algorithm. Our approach is based on the exact reproduction of the continuous coupling function in the original quantum impurity model. It augments each chain site of the Wilson chain by a coupling to an additional reservoir. This open Wilson chain is constructed by a continuous fraction expansion and the coupling function is treated in second order in the context of the Bloch-Redfield approach. The eigenvalues of the resulting Bloch-Redfield tensor generate a finite life time of the numerical renormalization group excitations that leads to a natural broadening of the spectral functions. We combine this approach with z-averaging and an analytical exact expression for the correlation part of the self-energy to obtain an accurate representation of the spectral function of the original continuum model in the absence and presence of an external magnetic field.