Boson correlation energies via variational minimization with the two-particle reduced density matrix: Exact N-representability conditions for harmonic interactions

The ground-state energies of systems of N bosons with pairwise interactions were calculated through the variational minimization of the energy with respect to the two-particle reduced-density matrix (2-RDM). The results of the calculations indicate that within round-off error that two-positivity is exact for systems of bosons with harmonic interactions. The enforcement of two-positivity on the 2-RDM through the D and G conditions was found to produce exact energies for all perturbation strengths in the limit of sufficiently large one-particle rank. The two-positivity conditions were found to be exact for several classes of Hamiltonians with two-particle interactions.