Beyond a Richardson–Gaudin Mean-Field: Slater–Condon Rules and Perturbation Theory

Richardson–Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson–Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater–Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson–Gaudin states while being feasible to compute.