Exact Solution of a Hubbard Chain with Bond-Charge Interaction

We obtain the exact solution of a general Hubbard chain with kinetic energy $t$, bond-charge interaction $X$, and on-site repulsion $U$ with the only restriction $t=X$. At zero temperature and half filling, the model exhibits a Mott transition at $U=4t$. In the metallic phase and near half filling, superconducting states are part of the degenerate ground state and are favored for small $U$ if the system is slightly perturbed.