A study of the Hubbard model on ladders and layers by means of the COM is reported in Refs. [72,73]. In particular the following properties have been computed:
The COM results have been analyzed in relation with:
We proposed a theoretical framework to describe the ladder and layer systems. In this scheme of calculations, the single-particle Green's function for any number of coupled chains and planes is obtained by solving self-consistently a system of integral equations.
As preliminary study of the two-leg ladder system , the behavior of the chemical potential as a function of the ratio has been analyzed. The sharp feature we found around could indicate the onset of some spin ordering related to the increasing of frustration in the spin coupling channel due to the appearance of an additional exchange interaction along the rungs.
For the two-plane layer system , we have studied the behavior of the uniform static susceptibility as a function of the filling and the temperature . The results obtained have been compared to those experimentally observed in [74,75] and others double-layered materials with a overall qualitative agreement.