A density matrix functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the system as the two-body interaction and particle number vary. The application of density matrix functional theory to the Lipkin model illustrates that it could be a valuable tool for systems presenting a shape phase transition such as nuclei. The improvement of one-body observables description as well as the interest for energy density functional theory are discussed.

• Received 7 October 2008

DOI:https://doi.org/10.1103/PhysRevC.79.014301