The wavefunction renormalization constant for the one- and two- band   Hubbard hamiltonians in two dimensions
  The wavefunction renormalization in the Hubbard model is studied, by using well tested mean field tecniques. The 'orthogonality catastrophe' is shown to exist, even in 2D, for doping levels sufficiently close to half filling. The results are extended beyond mean field, by constructing delocalized wavefunctions, with the correct symmetries of the exact solutions. The physics are still well described by the assumption of the existence of the orthogonality catastrophe. 
E. Louis, G. Chiappe, J. Galan, F. Guinea and J. A. Verges