Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors

TL;DR

This paper introduces a Krylov-space method for calculating spectral functions within the DMRG framework, demonstrating improved accuracy and efficiency over traditional approaches for various condensed matter models.

Contribution

It proposes a Krylov-space approach for the correction-vector method in DMRG, enhancing accuracy and efficiency in spectral function calculations.

Findings

Krylov-space approach can outperform conjugate gradient in accuracy and efficiency.

Using Krylov-space decomposition for ground state DMRG improves error integration.

Validated on Heisenberg, t-J, and Hubbard models.

Abstract

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction-vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that Krylov-space approach can be more accurate and efficient than conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.