  The variational reduced density matrix theory has been recently applied with
great success to models within the truncated doubly-occupied configuration
interaction space, which corresponds to the seniority zero subspace.
Conservation of the seniority quantum number restricts the Hamiltonians to be
based on the SU(2) algebra. Among them there is a whole family of exactly
solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational
theory against two different exactly solvable models, the
Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact
numerical results for the so-called PQGT N-representability conditions in both
cases for systems that go from 10 to 100 particles. However, when random
single-particle energies as appropriate for small superconducting grains are
considered, the exactness is lost but still a high accuracy is obtained.
