Uncertainty relations and reduced density matrices: Mapping many-body quantum mechanics onto four particles - art. no. 042113

For the description of ground-state correlation phenomena an accurate mappi ng of many-body quantum mechanics onto four particles is developed. The ene rgy for a quantum system with no more than two-particle interactions may be expressed in terms of a two-particle reduced density matrix (2-RDM), but v ariational optimization of the 2-RDM requires that it corresponds to an N-p article wave function. We derive N-representability conditions on the 2-RDM that guarantee the validity of the uncertainty relations for all operators with two-particle interactions. One of these conditions is shown to be nec essary and sufficient to make the RDM solutions of the dispersion condition equivalent to those from the contracted Schrodinger equation (CSE) [Mazzio tti, Phys. Rev. A 57, 4219 (1998)]. In general, the CSE is a stronger N-rep resentability condition than the dispersion condition because the CSE impli es the dispersion condition as well as additional N-representability constr aints from the Hellmann-Feynman theorem. Energy minimization subject to the representability constraints is performed for a boson model with 10, 30, a nd 75 particles. Even when traditional wave-function methods fail at large perturbations, the present method yields correlation energies within 2%.