RENORMALIZED LINKED-CLUSTER EXPANSION FOR STRONGLY CORRELATED LATTICE FERMIONS IN D=INFINITY DIMENSIONS

We show that mean-field-type symmetry-breaking approximations for correlated fermions can be constructed by performing vertex renormalization (VR) in the linked-cluster expansion, just as for the case of lattice spin models. In the limit of infinite spatial dimensions we sum up exactly the renormalized diagrams for the grand-canonical potential of the Hubbard model and, using the diagrammatic technique for Hubbard operators, we construct explicitly an approximate VR. The procedure leads to a self-consistent symmetry breaking analogous to that of the mean-field theory for spin systems. We present solutions for the case of half-filled energy band. They are valid for arbitrary temperatures and become exact for both large-U limit and for U = 0. The antiferromagnetic order parameter is found to have the conventional mean-field form and, in the regime of strong correlations, the obtained critical temperature coincides with the mean-field-theory result for the Neel temperature of the effective Heisenberg Hamiltonian.