Spectral functions for single- and multi-Impurity models using DMRG

TL;DR

This paper introduces a new method using the Lehmann formula within DMRG to accurately compute spectral functions for impurity models, overcoming limitations of the correction vector approach and enabling better analysis of excitation spectra.

Contribution

The authors develop a novel approach to calculate peak spectra from DMRG data, providing a more accurate deconvolution of spectral functions for impurity models.

Findings

The new method accurately approximates deconvoluted spectral functions.

Application to three coupled Anderson impurities demonstrates effectiveness.

The approach can be adapted to lattice models beyond impurity systems.

Abstract

This article focuses on the calculation of spectral functions for single- and multi-impurity models using the density matrix renormalization group (DMRG). To calculate spectral functions from DMRG, the correction vector method is presently the most widely used approach. One, however, always obtains Lorentzian convoluted spectral functions, which in applications like the dynamical mean-field theory can lead to wrong results. In order to overcome this restriction we show how to use the Lehmann formula to calculate a peak spectrum for the spectral function. We show that this peak spectrum is a very good approximation to a deconvolution of the correction vector spectral function. Calculating this deconvoluted spectrum directly from the DMRG basis set and operators is the most natural approach, because it uses only information from the system itself. Having calculated this excitation spectrum, one can use an arbitrary broadening to obtain a smooth spectral function, or directly analyze the excitations. As a nontrivial test we apply this method to obtain spectral functions for a model of three coupled Anderson impurities. Although, we are focusing in this article on impurity models, the proposed method for calculating the peak spectrum can be easily adapted to usual lattice models.