Repository: Freie Universität Berlin, Math Department

Fast Optical Absorption Spectra Calculations for Periodic Solid State Systems

Henneke, F. and Lin, L. and Vorwerk, C. and Draxl, C. and Klein, R. and Yang, C. (2020) Fast Optical Absorption Spectra Calculations for Periodic Solid State Systems. Communications in Applied Mathematics and Computational Science, 15 (1). pp. 89-113.

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We present a method to construct an efficient approximation to the bare exchange andscreened direct interaction kernels of the Bethe-Salpeter Hamiltonian for periodic solid state systemsvia the interpolative separable density fitting technique. We show that the cost of constructing the approximate Bethe-Salpeter Hamiltonian scales nearly optimally asO(Nk) with respect to thenumber of samples in the Brillouin zoneNk. In addition, we show that the cost for applying the Bethe-Salpeter Hamiltonian to a vector scales asO(NklogNk). 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 theO(N2k) andO(N3k) 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-dimensionalmodel problems and three-dimensional real materials (graphene and diamond). For the diamond system withNk= 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.

Item Type:Article
Uncontrolled Keywords:Bethe–Salpeter equation, interpolative separable density fitting, optical absorptionfunction
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2422
Deposited By: Ulrike Eickers
Deposited On:02 Apr 2020 07:12
Last Modified:15 Sep 2020 05:04

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