Dynamical density-matrix renormalization-group method

TL;DR

This paper introduces a simplified and more accurate dynamical density-matrix renormalization-group (DMRG) method for calculating spectral functions and excited states in low-dimensional quantum systems, demonstrated on the Peierls-Hubbard model.

Contribution

A new dynamical DMRG formulation based on an exact variational principle, improving simplicity and accuracy over previous correction vector methods.

Findings

Spectral functions of infinite systems are accurately reproduced.

Finite-size scaling of spectral functions is effectively analyzed.

The optical conductivity spectrum of the Mott-Peierls insulator differs from other insulator types.

Abstract

I present a density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum.The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.