Charge order and antiferromagnetic order in the Hubbard model with nearest-neighbor Coulomb interaction: Weak coupling

The half-filled-band Hubbard model with an added Coulomb repulsion between electrons on nearest-neighbor sites is studied. We investigate the existence of Hartree-Fock self-consistent solutions which break the symmetry between even and odd sites: these are of the antiferromagnetic and charge-order type. Emphasis is put on the large-bandwidth (weak-coupling) regime where we find BCS-like gap equations and critical temperatures for the order parameters. At zero temperature, as the parameters of the Hamiltonian are altered, the system exhibits a first-order phase transition from an antiferromagnetic to a charge-ordered state. The two kinds of order never coexist.