Translator Disclaimer
2020 Fast optical absorption spectra calculations for periodic solid state systems
Felix Henneke, Lin Lin, Christian Vorwerk, Claudia Draxl, Rupert Klein, Chao Yang
Commun. Appl. Math. Comput. Sci. 15(1): 89-113 (2020). DOI: 10.2140/camcos.2020.15.89


We present a method to construct an efficient approximation to the bare exchange and screened direct interaction kernels of the Bethe–Salpeter Hamiltonian for periodic solid state systems via the interpolative separable density fitting technique. We show that the cost of constructing the approximate Bethe–Salpeter Hamiltonian can be reduced to nearly optimal as 𝒪(Nk) with respect to the number of samples in the Brillouin zone Nk for the first time. In addition, we show that the cost for applying the Bethe–Salpeter Hamiltonian to a vector scales as 𝒪(Nk logNk). Therefore, the optical absorption spectrum, as well as selected excitation energies, can be efficiently computed via iterative methods such as the Lanczos method. This is a significant reduction from the 𝒪(Nk2) and 𝒪(Nk3) scaling associated with a brute force approach for constructing the Hamiltonian and diagonalizing the Hamiltonian, respectively. We demonstrate the efficiency and accuracy of this approach with both one-dimensional model problems and three-dimensional real materials (graphene and diamond). For the diamond system with Nk=2197, it takes 6 hours to assemble the Bethe–Salpeter Hamiltonian and 4 hours to fully diagonalize the Hamiltonian using 169 cores when the brute force approach is used. The new method takes less than 3 minutes to set up the Hamiltonian and 24 minutes to compute the absorption spectrum on a single core.


Download Citation

Felix Henneke. Lin Lin. Christian Vorwerk. Claudia Draxl. Rupert Klein. Chao Yang. "Fast optical absorption spectra calculations for periodic solid state systems." Commun. Appl. Math. Comput. Sci. 15 (1) 89 - 113, 2020.


Received: 10 December 2019; Accepted: 3 March 2020; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07224511
MathSciNet: MR4113785
Digital Object Identifier: 10.2140/camcos.2020.15.89

Primary: 65F15, 65Z05

Rights: Copyright © 2020 Mathematical Sciences Publishers


This article is only available to subscribers.
It is not available for individual sale.

Vol.15 • No. 1 • 2020
Back to Top