Symmetry crossover and excitation thresholds at the neutral-ionic   transition of the modified Hubbard model
  Exact ground states, charge densities and excitation energies are found using valence bond methods for N-site modified Hubbard models with uniform spacing. At the neutral-ionic transition (NIT), the ground state has a symmetry crossover in 4n, 4n+2 rings with periodic and antiperiodic boundary conditions, respectively. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS) and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to about 0.1t of the symmetry crossover. The NIT is interpreted as a localized ground state (gs) with finite gaps on the paired side and an extended gs with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic gs at the transition that, however, is unconditionally unstable to dimerization. 
Y. Anusooya-Pati (1), Z.G. Soos (1), A.Painelli (2) ((1) Princeton   Univ., (2) Parma Univ.)