Strongly interacting Luttinger liquid and superconductivity in an exactly solvable model

A 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 strongly interacting Luttinger liquid can be realized in superconducting state at a high electron density and high value of repulsive on-site Coulomb interaction