A structure preserving Lanczos algorithm for computing the optical absorption spectrum

TL;DR

This paper introduces a novel structure preserving Lanczos algorithm tailored for efficiently approximating the optical absorption spectrum by leveraging the block structure of Bethe--Salpeter Hamiltonian matrices and incorporating generalized averaged Gauss quadrature.

Contribution

The paper presents a new structure preserving Lanczos algorithm that improves the approximation of optical absorption spectra without Tamm--Dancoff approximation, exploiting matrix structure and accelerating convergence.

Findings

Effective in approximating optical absorption spectra

Outperforms existing methods in convergence speed

Numerical examples confirm accuracy and efficiency

Abstract

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.