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. Thehc/2eperiodicity of the ground-state energy with respect to a flux &Fgr; 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&Fgr;=0limit. In addition, the new states that were missing in the Lieb–Wu solution are derived. ©1998 American Institute of Physics.