Performances in solving the Bethe-Salpeter equation with the Yambo code

Abstract: In this work, we analyze the performances of two different strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The first strategy employs direct diagonalization, while the second is based on an iterative solver. The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. We consider both the hermitian (Tamm-Dancoff approximation) and pseudo-hermitian forms, addressing dense matrices of three different sizes. A description of the implementation is also provided, with details for the pseudo-hermitian case. Timing and memory utilization are analyzed on both CPU and GPU clusters. The CPU simulations are performed on a local cluster in Rome, while the GPU simulations are performed on the Leonardo HPC cluster of CINECA. Our results demonstrate that it is now feasible to handle dense BSE matrices of the order 10$^5$.