GPU-Accelerated Solution of the Bethe-Salpeter Equation for Large and Heterogeneous Systems

Area of Science:

• Computational Physics
• Materials Science
• Quantum Chemistry

Background:

• Accurate calculation of material properties like excitation energies and optical spectra is essential for materials design.
• Traditional methods for solving the Bethe-Salpeter equation (BSE) are computationally intensive, limiting system sizes.
• Density functional theory (DFT) provides a foundation but requires post-processing for excited-state properties.

Purpose of the Study:

• To present a massively parallel, GPU-accelerated implementation of the Bethe-Salpeter equation (BSE).
• To enable efficient and accurate computation of vertical excitation energies (VEEs) and optical absorption spectra for large condensed and molecular systems.
• To investigate the impact of system size and defect interactions on material properties.

Main Methods:

• Developed a GPU-accelerated BSE solver utilizing density matrix perturbation theory and low-rank decomposition of the screened Coulomb interaction.
• Implemented algorithms to circumvent slow convergence issues with empty/occupied states and large dielectric matrix inversions.
• Exploited the nearsightedness of the density matrix for semiconductors and insulators to reduce computational cost.
• Employed a hierarchical loop and data distribution strategy for scaling calculations to thousands of GPUs.

Main Results:

• Demonstrated the method's efficacy by computing VEEs for spin defects in wide-band-gap materials, requiring supercells up to 1000 atoms for convergence.
• Validated the accuracy of the GW-BSE approach on large systems.
• Analyzed the symmetry breaking of triplet states in a diamond lattice with 1727 atoms due to defect interactions.

Conclusions:

• The developed GPU-accelerated BSE method offers significant computational savings and enables accurate calculations for large, complex material systems.
• Supercell sizes of up to 1000 atoms are necessary for converged VEE calculations in certain materials.
• The study provides insights into defect interactions and their influence on electronic and optical properties, particularly symmetry breaking in triplet states.