Efficient Trilinear Interpolation Technique for Bethe-Salpeter Calculations of Optical Spectra

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, with very heavy computational load, preventing access to numerous derived quantities, as e.g. Raman intensities [1]. We present a new methodology that allows to decrease the work load to reach a given accuracy. This technique is based on a trilinear interpolation technique within the Brillouin zone, combined with the Lanczos algorithm and double-grid technique, in the spirit of Refs. [2] and [3], to achieve efficient speed-up and memory use. The technique is benchmarked in terms of accuracy on selected test cases. The scaling has also been studied from low to very-high density of points in the Brillouin Zone, showing a much better scaling than a complete Bethe-Salpeter. This approach might be used in the future for more complex calculations of optical properties. References [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).