Large-scale parallel null space calculation for nuclear configuration interaction

One of the emerging computational approaches in nuclear physics is the configuration interaction (CI) method for solving the many-body nuclear Hamiltonian in a sufficiently large single-particle basis space to obtain exact answers - either directly or by extrapolation. One particular goal is to compute a number of lowest eigen-values and eigenvectors of the Hamiltonian Ĥ that are associated with a fixed total angular momentum J. To achieve this goal, we perform a simultaneous diagonalization of Ĥ and Ĵ², where Ĵ² is the total angular momentum square operator. In this approach, we first compute the invariant subspace of Ĵ² corresponding to a fixed and known eigenvalue λ = J (J + 1), and then project Ĥ into this subspace in order to extract desired spectral information from the resulting lower dimensional Hamiltonian. In this paper, we discuss how to compute the desired invariant subspace of Ĵ² (or equivalently, the null space of Ĵ²-λl) efficiently on a large-scale distributed-memory high performance computer. We describe both the algorithms we use to solve the problem and implementation details that allow us to achieve optimal performance. We demonstrate the performance of our implementation by numerical experiments conducted for a few light nuclei.