A study of the t-t'-U model in the paramagnetic phase by means of the COM is reported in Refs. [80,81,82,83]. In particular the following properties have been computed:
The COM results have been compared with the ones obtained by:
The COM results have been analyzed in relation with the ones obtained by:
The effect of the bare parameter, whose value is considered to be material dependent for the high-T cuprate superconductors, has been analyzed in detail. Our scheme of calculation can reproduce with good accuracy the results of numerical simulation for some local and integrated quantities [80,83]. We have computed the structure of the energy bands, the shape of the Fermi surface and the relative position of the van Hove singularity. The comparison with experimental data has shown that the Hubbard model is capable to describe both and , that share the property to be 1-layer cuprates. On the contrary, it does not seem the case for that is a 2-layer cuprate . This can be read as a clear signal that two-dimensional Hubbard-like models can play an important role in describing the physics of the $1$-layer cuprates superconductors, but that the multi-layer ones need some more complex models. We have also shown that the - - model presents an incommensurate phase at finite doping and that the magnetic scattering become isotropic as is increased . The occurrence of such an evolution of the magnetic fluctuations can be related to the spreading of the nesting vector in momentum space. That is, the evolution from a pseudo-nested to a roughly circular hole-like Fermi surface. Indeed, the main result is that a scenario emerges where the shape of the Fermi Surface and the incommensurate spin fluctuations are connected, showing that ARPES and neutron scattering experiments are intimately related. The results obtained are in qualitative agreement with the experimental situation observed in compounds.