FAST OPTICAL ABSORPTION SPECTRA CALCULATIONS FOR PERIODIC SOLID STATE SYSTEMS

摘要

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(N-k) with respect to the number of samples in the Brillouin zone N-k for the first time. In addition, we show that the cost for applying the Bethe-Salpeter Hamiltonian to a vector scales as O(N-k log N-k). 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(N-k(2)) and O(N-k(3)) 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 N-k = 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.