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Recent progress on the Bethe--Salpeter eigenvalue problem
2018-01-01 12:13  »ª¶«Ê¦·¶´óÑ§

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ÕªÒª : In electronic structure calculations, excited state properties of molecules and solids can be obtained by solving the Bethe--Salpeter equation (BSE). Discretization of the BSE leads to a structured non-Hermitian dense eigenvalue problem with a special 2-by-2 block structure. In principle all excitation energies are of interest. We first present a structure preserving algorithm that computes all eigenpairs of the BSE Hamiltonian. In some circumstances instead of computing each individual excitation energy, we need to estimate the optical absorption spectrum, which is a frequency dependent matrix functional and is measurable in optical absorption experiments. We propose a structure preserving Lanczos procedure to quickly compute the optical absorption spectrum. A recently developed technique of generalized averaged Gauss quadrature is also adopted to accelerate the convergence of the Lanczos algorithm.