A study of the attractive Hubbard model by means of the
*COM* is reported in
Refs. [76,77,78]. In
particular the following properties have been computed:

- The thermodynamic properties (i.e., double occupancy, crossover
temperature, chemical potential)
[76,77,78]
- The single-particle properties (i.e., density of states) [77,78]
- The response functions (i.e., spin susceptibility) [76,77,78]

The *COM* results have been compared with the ones
obtained by:

- Numerical techniques (i.e., Exact diagonalization, Lanczos and quantum Monte Carlo) [79].

The Hubbard model with on-site attractive interaction has been studied by means of the Composite Operator Method. At zero temperature, when the strength of the attractive interaction equals the bandwidth, the system exhibits a phase transition to a pair state, where all the electrons are locally paired [76]. The temperature which controls the crossover to the pair state is calculated as a function of . Some properties, as the double occupancy and the spin magnetic susceptibility [78], show a good agreement with numerical data. For strong attractive interaction the static uniform susceptibility is strongly depressed; increases by increasing and tends to zero as . Analytical and numerical calculations show that there is a critical value of the interaction, , where the system exhibits a metal-insulator transition. At zero temperature it is found that , where is the bandwidth [77].