Kadanoff-Baym equations and approximate double occupancy in a Hubbard dimer

We use the Kadanoff-Baym equations within the framework of many-body perturbation theory to study the double occupancies in a Hubbard dimer. The double occupancies are obtained from the equations of motion of the single-particle Green's function. Our calculations show that the approximate double occupancies can become negative. This is a shortcoming of approximate, and yet conserving, many-body self-energies. Among the tested perturbation schemes, the T-matrix approximation is the only one providing double occupancies which are always positive.