Hubbard Model with superconductivity aspects

The first followed the discovery of high-temperature superconductors in 1986. Until then, the Hubbard model was believed to have little to do with superconductivity. However, in the wake of the high-temperature superconductivity 'revolution', one particular adaptation of Hubbard's original model called the t-j model (originally arising in the context of doped Mott –Hubbard insulators) emerged as a compelling candidate for hosting a superconducting state. A rigorous proof of the existence (or non-existence) of a superconducting ground state in the t-j model is still missing underlying their research on superconductivity and the Hubbard model is continuing. (author)