Strongly Interacting Luttinger Liquid and Superconductivity in an   Exactly Solvable Model
  A new family of exactly solvable one dimensional models with a hard-core repulsive potential is solved by the Bethe Ansatz for an arbitrary hard-core radius. The exact ground state phase diagrams in a plane 'electron density - on-site interaction' have been studied for several values of a hard-core radius. It is shown that superconducting phase and strongly interacting Luttinger liquid state are coexisted at a high electron density and unusually high value of repulsive on-site Coulomb interaction. 
Igor N. Karnaukhov and Alexander A. Ovchinnikov