Deriving an extended one-band Hubbard model for cuprate superconductors

Abstract: The so-called three-band Hubbard model is generally believed to be a good model for fermions on a CuO 2 lattice and to contain key features allowing to understand high-temperature superconductivity in the cuprates. A simpler and more popular model is the one-band Hubbard model. In this thesis,an extended one-band Hubbard model is derived from the three-band model. First, some mathematical background is given, as well as an introduction to Hubbard-like models. Then, to derive the extended one-band Hubbard model, the CuO 2 lattice is divided into clusters of one Cu and two O sites, and a variant of the Feshbach method is used to replace each such cluster by a single lattice site. To nd a suitable one-band model, all Hamiltonian matrix elements are matched between the two models. Finally, dierent sets of three-band parameters are considered, and it is studied how this aects the parameters in the extended one-band Hubbard model.