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

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