Boson correlation energies and density matrices from reduced Hamiltonian interpolation

The ground-state energies of interacting bosons are computed beyond the mean-field approximation by a new method known as reduced Hamiltonian interpolation (RHI) [D. A. Mazziotti and D. R. Herschbach, Phys. Rev. Lett. 83, 5185 (1999)]. In the RHI, the N-particle Hamiltonian is represented through a sequence of p-particle expanded and reduced Hamiltonians that give upper and lower bounds on the true energy. Assimilating ideas from N representability and dimensional interpolation, the RHI technique interpolates over the number p of quasiparticles to determine the N-particle energy with close upper and lower bounds. With the Hellmann-Feynman theorem, we extend the RHI to compute the two-particle reduced density matrix (2RDM) as well as the energy. We examine both the computational advantages of RHI in comparison with traditional methods and the possibility of extending the RHI to treat fermion correlation. Applied to bosons with harmonic interactions as well as a two-level system, the RHI technique yields more than 99% of the correlation energy and an accurate correlation correction for the elements of the 2RDM.