Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions

TL;DR

This paper introduces a reorthonormalization method for Chebyshev matrix product states that enhances the accuracy of dynamical correlation function calculations by correcting orthogonality errors in the polynomial recurrence.

Contribution

It proposes a reorthonormalization technique to address orthogonality loss in Chebyshev MPS, improving the precision of dynamical correlation functions.

Findings

Significant accuracy improvement demonstrated on XY and Heisenberg models.

Reorthonormalization reduces cumulative errors in Chebyshev expansions.

Method enhances the reliability of MPS-based dynamical calculations.

Abstract

The Chebyshev expansion offers a numerically efficient and easy-implement algorithm for evaluating dynamic correlation functions using matrix product states (MPS). In this approach, each recursively generated Chebyshev vector is approximately represented by an MPS. However, the recurrence relations of Chebyshev polynomials are broken by the approximation, leading to an error which is accumulated with the increase of the order of expansion. Here we propose a reorthonormalization approach to remove this error introduced in the loss of orthogonality of the Chebyshev polynomials. Our approach, as illustrated by comparison with the exact results for the one-dimensional XY and Heisenberg models, improves significantly the accuracy in the calculation of dynamical correlation functions.