Application of the ChASE eigensolver to excitonic Hamiltonians

Numerically solving the Bethe-Salpeter equation for the optical polarization function is a very successful approach for describing excitonic effects in first-principles simulations of materials. Converged results for optical spectra and exciton binding energies are directly comparable to experiment and are of predictive quality, thus allowing for computational materials design. However, these accurate results come at high computational cost: For modern complex materials this approach leads to large, dense matrices with sizes reaching up to n~400k. Since the experimentally most relevant exciton binding energies require only the lowest eigenpairs of these matrices, iterative schemes are a feasible alternative to prohibitively expensive direct diagonalization.The Chebyshev Accelerated Subspace iteration Eigensolver (ChASE), which is developed at JSC, is an ideal solver for solving such large dense eigenvalue problems. ChASE leverages on the preponderant use of BLAS 3 subroutines to achieve close-to-peak performance. Moreover, the code is parallelized for many- and multi-core platforms. In the initial phase of the project we are conducting feasibility tests comparing the shared memory parallelization of ChASE with the state-of-the-art direct eigensolver on problems ranging from n~20k up to n~60k. The long-term objective is to develop a distributed CPU/GPU parallelization of ChASE in order to solve larger eigenproblems by effectively exploiting heterogeneous multi-GPU architectures