Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation

TL;DR

This paper introduces a double-grid method combined with Wannier interpolation to significantly reduce the computational cost of solving the Bethe-Salpeter equation for optical spectra in semiconductors.

Contribution

The authors develop and validate a novel double-grid technique with Wannier interpolation to accelerate Bethe-Salpeter equation calculations.

Findings

Substantial computational speed-up achieved for GaAs and Si.

Accurate optical spectra obtained with fewer k-points.

Method enables application to larger, complex systems.

Abstract

The Bethe-Salpeter equation is a widely used approach to describe optical excitations in bulk semiconductors. It leads to spectra that are in very good agreement with experiment, but the price to pay for such accuracy is a very high computational burden. One of the main bottlenecks is the large number of k-points required to obtain converged spectra. In order to circumvent this problem we propose a strategy to solve the Bethe-Salpeter equation based on a double-grid technique coupled to a Wannier interpolation of the Kohn-Sham band structure. This strategy is then benchmarked for a particularly difficult case, the calculation of the absorption spectrum of GaAs, and for the well studied case of Si. The considerable gains observed in these cases fully validate our approach, and open the way for the application of the Bethe-Salpeter equation to large and complex systems.