Novel Trilinear Interpolation Technique to Improve the Convergence Rate of Bethe-Salpeter Calculations

Gillet, Yannick [UCL] Giantomassi, Matteo [UCL] Gonze, Xavier [UCL]

The inclusion of excitonic effects in semiconductors with the Bethe-Salpeter equation leads to good agreement of the optical spectra with experimental measurements. However, this approach requires in general very fine meshes of wavevectors in the Brillouin Zone in order to obtain well-converged spectra, preventing access to numerous derived quantities, as depicted e.g. in [1]. Rohlfing [2] and Kammerlander [3] have proposed different techniques to treat such fine meshes, allowing to decrease the work load to reach a given accuracy. We have designed a new methodology, based on a trilinear interpolation technique within the Brillouin zone, combined with the Lanczos algorithm, also incorporating ideas from Ref. [2,3], like a double-grid technique, to achieve superiour speed-up and memory use. We describe the implementation, and show results for selected materials. [1] Y. Gillet, M. Giantomassi and X. Gonze, Phys. Rev. B 88, 094305 (2013) [2] M. Rohlfing and S.G. Louie, Phys. Rev. B 62, 4927 (2000) [3] D. Kammerlander, S. Botti, M.A.L. Marques, A. Marini and C. Attaccalite, Phys. Rev. B 86, 125203 (2012)