Spectral functions for single- and multi-impurity models using density matrix renormalization group

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 in 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 use chain decompositions in which the resulting effective Hamiltonian can be diagonalized completely to calculate a discrete ``peak'' spectrum. 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.