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Shao, Meiyue; da Jornada, Felipe H.; Lin, Lin; Yang, Chao; Deslippe, Jack; Louie, Steven G.

A structure preserving Lanczos algorithm for computing the optical absorption spectrum. (English) Zbl 1391.65089

SIAM J. Matrix Anal. Appl. 39, No. 2, 683-711 (2018).
Summary: We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving the full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

Cited in 1 Review
Cited in 6 Documents

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F60 Numerical computation of matrix exponential and similar matrix functions

Keywords:

Bethe-Salpeter equation; Tamm-Dancoff approximation; optical absorption spectrum; Lanczos procedure; structure preserving algorithm; matrix functional; Gauss quadrature

Software:

TurboEELS; BSEPACK; BerkeleyGW
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\textit{M. Shao} et al., SIAM J. Matrix Anal. Appl. 39, No. 2, 683--711 (2018; Zbl 1391.65089)
Full Text: DOI arXiv

References:

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