Gapped-filtering for efficient Chebyshev expansion of the density projection operator

TL;DR

The paper introduces gapped-filtering, a method that enhances the efficiency of Chebyshev expansions for density matrices by focusing on energy regions outside spectral gaps, reducing computational effort especially in high-accuracy scenarios.

Contribution

It presents a novel gapped-filtering technique that optimizes Chebyshev coefficients to accurately represent the density matrix while reducing computational complexity.

Findings

Reduces Chebyshev expansion terms by factors of 2-3 for high accuracy.

Efficiently determines the HOMO and LUMO positions for the method.

Improves stochastic-GW calculation efficiency.

Abstract

We develop the gapped-filtering method, whereby a short Chebyshev expansion accurately represents the density-matrix operator. The method optimizes the Chebyshev coefficients to give the correct density matrix at all energies except within the gapped region where there are no eigenstates. Gapped filtering reduces the number of required terms in the Chebyshev expansion compared to traditional expansion methods, as long as one knows or can determine efficiently the HOMO and LUMO positions. The reduction is especially noticeable (factors of 2-3) when high accuracy is sought. To exemplify the method, we use gapped-filtering to increase the efficiency of stochastic-GW calculations.