Graph-based block-diagonalization of full configuration interaction Hamiltonian

We developed a graph-based block-diagonalization (GBBD) method for the full configuration interaction (FCI) Hamiltonian of molecular systems to efficiently calculate the exact eigenvalues of low-energy states. In this approach, the non-zero matrix elements of the Hamiltonian are represented as edges on a graph, which naturally decomposes into disconnected clusters. Each cluster corresponds to an independent block in the block-diagonalized form of the Hamiltonian. The eigenvalues in the low-energy sector were obtained by solving the eigenvalue problem for each block matrix and by solving a modified Hamiltonian subject to orthonormality constraints with respect to previously computed lower-energy eigenstates. An advantage of our method is that, compared to the conventional FCI approach, it can rapidly compute the low-lying eigenvalues and eigenvectors through graph analysis while saving memory and without the need to compute all edges. We applied the GBBD method to linear hydrogen H chains and the N2 molecule. The results showed excellent agreement with the exact ones, confirming both the accuracy and efficiency of the proposed method. Finally, we discussed several physical properties in relation to the number of H2 chains and for the N2 molecule.