Dynamical Correlation Functions using the Density Matrix Renormalization Group

TL;DR

This paper explores two methods to extend the DMRG technique for calculating dynamical correlation functions in low-dimensional strongly correlated systems, focusing on accuracy and computational efficiency.

Contribution

It introduces and compares the Lanczos vector method and the correction vector method for dynamical DMRG calculations, highlighting their advantages and limitations.

Findings

Lanczos vector method is fast but less accurate at high frequencies.

Correction vector method achieves high accuracy at specific frequencies.

Frequency interpolation allows reconstruction of dynamical spectra.

Abstract

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.