A structure preserving Lanczos algorithm for computing the optical absorption spectrum
For computational materials science researchers, this provides a more efficient method for optical spectrum calculations, but the improvement is incremental over existing Lanczos-based approaches.
The paper presents a structure preserving Lanczos algorithm for computing the optical absorption spectrum from the Bethe-Salpeter equation without the Tamm-Dancoff approximation, incorporating generalized averaged Gauss quadrature to accelerate convergence. Numerical examples demonstrate its effectiveness.
We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving 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.