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

Abstract

By combining Wilson's numerical renormalization group (NRG) with a modified Bloch-Redfield approach (BRA), we are able to eliminate the artificial broadening of the Lehmann representation of quantum impurity spectral functions required by the standard NRG 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 BRA. The eigenvalues of the resulting Bloch-Redfield tensor generate a finite lifetime of the NRG 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.