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

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We developed a GPU-accelerated Bethe-Salpeter equation (BSE) method to efficiently calculate excitation energies and optical spectra for materials. This approach enables accurate simulations of large systems, crucial for understanding material properties.

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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.