Large-scale parallel exact diagonalization algorithm of the Hubbard model on Tianhe-2 supercomputer

Abstract

We propose a parallel exact diagonalization method for solving the large-scale Hubbard model. The core of this algorithm is the parallelization of the Lanczos algorithm, for which we propose a hierarchical communication model and a fast strategy for finding nonzero elements of large-scale matrix, starting only from the symmetry of Hamiltonian matrix. The effect of our parallel algorithm was tested on the Tianhe-2 supercomputer, where the strong scaling efficiency could reach 53% for 30,000 cores in a 140-billion dimensional matrix, and the weak scaling efficiency remained above 40% for 60,000 cores in a 730-billion dimensional matrix.