Bound electron pairs in strongly correlated models of high-temperature superconductivity

The ground-state energy of two electrons on a ring is calculated for the one-dimensional Hubbard model with positive and negative on-site interaction and for the contraction model with additive and multiplicative interaction terms. The hc/2e periodicity of the ground-state energy with respect to a flux Φ threading the loop is derived. The periodicity may serve as an indication of superconductivity. The results are shown to be consistent with the Lieb-Wu solution for Φ=0 limit. In addition, the new states that were missing in the Lieb-Wu solution are derived.