Efficient On-the-Fly Interpolation Technique for Bethe-Salpeter Calculations of Optical Spectra

TL;DR

This paper introduces a new on-the-fly interpolation method combined with the Lanczos algorithm that significantly speeds up Bethe-Salpeter calculations of optical spectra, reducing computational resources needed.

Contribution

It presents a novel double-grid interpolation technique that improves convergence efficiency and reduces memory usage in Bethe-Salpeter calculations for crystalline systems.

Findings

Achieves significant speed-up in calculations

Reduces memory requirements substantially

Demonstrates better scaling than traditional methods

Abstract

The Bethe-Salpeter formalism represents the most accurate method available nowadays for computing neutral excitation energies and optical spectra of crystalline systems from first principles. Bethe-Salpeter calculations yield very good agreement with experiment but are notoriously difficult to converge with respect to the sampling of the electronic wavevectors. Well-converged spectra therefore require significant computational and memory resources, even by today's standards. These bottlenecks hinder the investigation of systems of great technological interest. They are also barriers to the study of derived quantities like piezoreflectance, thermoreflectance or resonant Raman intensities. We present a new methodology that decreases the workload needed to reach a given accuracy. It is based on a double-grid on-the-fly interpolation within the Brillouin zone, combined with the Lanczos algorithm. It achieves significant speed-up and reduction of memory requirements. The technique is benchmarked in terms of accuracy on silicon, gallium arsenide and lithium fluoride. The scaling of the performance of the method as a function of the Brillouin Zone point density is much better than a conventional implementation. We also compare our method with other similar techniques proposed in the literature.