Double k-Grid Method for Solving the Bethe-Salpeter Equation via Lanczos Approaches

Area of Science:

• Computational materials science
• Condensed matter physics
• Quantum chemistry

Background:

• Calculating optical spectra of periodic crystals via the Bethe-Salpeter equation (BSE) is computationally intensive.
• Convergence of k-points sampling grids in the Brillouin zone is a major bottleneck.

Purpose of the Study:

• To propose an efficient double k-grid approach for k-sampling in BSE calculations.
• To improve the computational tractability of optical spectra calculations for periodic crystals.

Main Methods:

• A double k-grid approach is introduced, compatible with the Lanczos-based Haydock iterative solution.
• A coarse k-grid controls computational cost, while a dense k-grid captures excitonic effects.
• The method requires minimal extra computation and is straightforward to implement.

Main Results:

• Optical spectra calculations were performed on bulk Silicon (Si), bulk Gallium Arsenide (GaAs), and monolayer Molybdenum Disulfide (MoS2).
• The obtained spectra showed good agreement with previously reported data.
• The double k-grid approach demonstrated improved efficiency and accuracy.

Conclusions:

• The proposed double k-grid method offers a computationally efficient pathway for BSE calculations.
• This framework can enable optical spectra calculations for large-scale systems with stringent k-sampling requirements.
• The approach has the potential to significantly advance materials science research.