In 1986, Bednorz and Müller discovered high-Tcsuperconductivity in La-based cuprate compounds (e.g.La2−x[Ba,Sr]xCuO4) [1]. These materials have a layered body-centered tetragonal structure (BCT) consist-ing of CuO2planes separated by charge reservoir layers which may dope electrons or holes into the CuO2layers rending them conducting. Early, in order to understand the underlying mechanism of unconventional superconductivity, P. W. Anderson [2] proposed that essential physics of cuprates would be captured by aone-band 2D Hubbard-like model in which the kinetic part is described by the nearest neighbor and thenext-nearest neighbor in-plane hopping amplitudes (t and t’), in addition to the Hubbard on-site U repulsive interaction that favors electron localization. However, recent density functional theory (DFT) calculations[3] and experimental (ARPES) investigations [4] have evidenced the three-dimensional character of theelectronic structure and the Fermi surface. Therefore, a 3D model accounting for the dispersion in the direction perpendicular to the CuO2layers is needed, and the subject of this work [9]