Large-Scale Exact Diagonalization Methods for the New Generation of Tianhe Supercomputing Systems

The exact diagonalization (ED) method, a key numerical technique in quantum and condensed matter physics, directly computes the ground state of quantum systems. This study leverages Hamiltonian matrix symmetry, matrix-free methods, hierarchical communication models, and a data-level parallel algorithm optimized for the MT-3000 architecture. We propose a heterogeneous parallel algorithm for large-scale sparse Hamiltonian matrix-vector multiplication on the new generation Tianhe supercomputing system, enabling large-scale exact diagonalization for the one-dimensional Hubbard model. Tests on the Tianhe new generation system show a strong scaling efficiency of 55.27% when scaling from 256 to 8192 processes for a 140-billion-dimension matrix. Weak scaling efficiency remains above 51.25% when scaling from 64 to 13 740 processes for a 730-billion-dimension matrix.