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

TL;DR

This paper introduces a GPU-accelerated, scalable method for solving the Bethe-Salpeter equation, enabling efficient calculation of excitation energies and optical spectra for large, complex systems, including defect-rich materials.

Contribution

It presents a novel GPU-based implementation that employs density matrix perturbation theory and low-rank Coulomb interaction decomposition for large-scale BSE calculations.

Findings

Successfully computed VEEs for systems with up to 1000 atoms.

Demonstrated the method's scalability to thousands of GPUs.

Validated the approach on defect-rich wide-band-gap materials.

Abstract

We present a massively parallel, GPU-accelerated implementation of the Bethe-Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting from single-particle eigenvalues and eigenvectors obtained with density functional theory. The algorithms adopted here circumvent the slowly converging sums over empty and occupied states and the inversion of large dielectric matrices, through a density matrix perturbation theory approach and a low-rank decomposition of the screened Coulomb interaction, respectively. Further computational savings are achieved by exploiting the nearsightedness of the density matrix of semiconductors and insulators to reduce the number of screened Coulomb integrals. We scale our calculations to thousands of GPUs with a hierarchical loop and data distribution strategy. The efficacy of our method is demonstrated by computing the VEEs of several spin defects in wide-band-gap materials, showing that supercells with up to 1000 atoms are necessary to obtain converged results. We discuss the validity of the common approximation that solves the BSE with truncated sums over empty and occupied states. We then apply our GW-BSE implementation to a diamond lattice with 1727 atoms to study the symmetry breaking of triplet states caused by the interaction of a point defect with an extended line defect.