From Hubbard model to t-J-U model: a canonical transformation formalism, the metal-insulator transition and mean-field state

We prove that the t-J-U model can be deduced from the Hubbard model at a large but finite U by a canonical transformation. We argue that the system may have a metal-insulator transition at a critical on-site Coulomb interaction whose value, however, is smaller than that in previous calculations in which the kinetic energy has a double counting. In a mean field theory and a special choice of the parameters, we show that the metallic state may be equivalent to the gossamer superconducting state proposed by Laughlin recently.