Transition density matrices of Richardson–Gaudin states

Recently, ground state eigenvectors of the reduced Bardeen–Cooper–Schrieffer (BCS) Hamiltonian, Richardson–Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This physically represents mean-field pairs electrons (geminals) with constant pairing strength. To move beyond mean-field, one must develop on basis all RG states. requires both practical expressions transition density matrices and an idea which states are most important in expansion. In this contribution, we present matrix elements calculate them numerically half-filled picket–fence models (reduced BCS energy spacing). There no Slater–Condon rules though analog aufbau principle proves to be useful choosing important.