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BIMSA Computational Math Seminar
Structure-preserving algorithms for the Bethe--Salpeter eigenvalue problem
Structure-preserving algorithms for the Bethe--Salpeter eigenvalue problem
Organizers
Zhen Li
,
Xin Liang
,
Zhi Ting Ma
,
Hamid Mofidi
,
Li Wang
,
Fan Sheng Xiong
,
Shuo Yang
,
Wu Yue Yang
Speaker
Meiyue Shao
Time
Thursday, June 19, 2025 3:00 PM - 4:00 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
In a molecular system the excitation of an electron is obtained by solving the so-called Bethe--Salpeter equation (BSE). Discretization of the Bethe--Salpeter equation leads to a dense non-Hermitian matrix eigenvalue problem with a special 2-by-2 block structure. In principle all excitation energies, i.e., all positive eigenvalues of the BSE Hamiltonian, are of interest. This is challenging in practice because the dimension of the BSE Hamiltonian depends quadratically on the number of electrons in the system. We developed a parallel structure preserving algorithm that computes all eigenpairs of the BSE Hamiltonian efficiently and accurately. In some circumstances, instead of computing each individual eigenpair, we need to compute the optical absorption spectrum, which is a frequency dependent matrix functional of the BSE Hamiltonian. We developed a Lanczos-type algorithm to efficiently compute the absorption spectrum without diagonalizing the BSE Hamiltonian. Parallel implementations of these algorithms are available in the software package BSEPACK.