A study of Mott transition in 2D and 3D Hubbard model by means of
the *COM* is reported in
Refs. [116,117]. In particular
the following properties have been computed:

- The thermodynamic properties (i.e., order parameter, phase diagram,
Mott gap, chemical potential, double occupancy)
[116,117]
- The single-particle properties (i.e., energy spectra, density of states) [116,117]

The Mott-Hubbard transition has been studied in the context of the two- and three- dimensional Hubbard model in Refs. [116] and [117], respectively. Analytical calculations show the existence of a critical value of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.