Fast Optical Absorption Spectra Calculations for Periodic Solid State Systems

Abstract

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.