A study of the 1D Hubbard model by means of the *COM*
is reported in
Refs. [19,20,21,22].
In particular, the following properties have been computed:

- Thermodynamic properties (i.e., chemical potential, ground state
energy, double occupancy, local magnetic moment, internal energy,
free energy, entropy, specific heat) in
Refs. [19,20,21,22]
- Single-particle properties (i.e., energy spectra, charge gap, momentum
distribution function, density of states) in
Refs. [19,20,22]
- Response functions (i.e., charge and spin correlations and susceptibilities, density distribution in real space) in Refs. [21,22]

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

- The Bethe Ansatz technique [23,24,25,26,27,28,29]
- Numerical techniques (i.e., Exact diagonalization, Lanczos and quantum
Monte Carlo)
[30,31,32,33]
- The Gutzwiller Approximation [34]
- The Ladder and the Self-Consistent Ladder Approximations [35]
- The Renormalization Group [36]

The Bethe Ansatz technique does not provide a complete framework
to study the 1D Hubbard model since it does allow the evaluation
of the response functions only in some limiting cases. According
to this, we have used the *COM*, within a two-pole
approximation, to study those properties which cannot be directly
extracted from the Bethe Ansatz. Firstly, we have compared our
results with the ones obtained by the Bethe Ansatz as well as by
other analytical and numerical approaches. At half filling, in
spite of considering a paramagnetic solution, we have found a
ground state with strong antiferromagnetic correlations
[19,20,22] in agreement with the exact
solution [23]. The energy spectra, in
proximity of half filling, clearly shows features (i.e., the
doubling of the Brillouin zone, the reflection of the upper band
and the bandwidth of the order ), which are due to strong
antiferromagnetic correlations. This antiferromagnetic-like state
also shows a gap for any value of the coupling
[20,22] in agreement with the
Bethe Ansatz result [23]. As function of
the Coulomb repulsion, the energy and double occupancy
[19,20,22] are in almost perfect
agreement with the exact ones. Such a good agreement is not
reached by other analytical approaches, like the Gutzwiller
approximation, the ladder and self-consistent ladder
approximations and the renormalization group. We have also
calculated the temperature dependence of the specific heat
[19,22]. The locations of the spin- and
charge- excitation peaks are consistent with the Bethe Ansatz ones
[28,29]. The behavior of the chemical
potential, for different values of temperature and Coulomb
potential, has been compared with both numerical and Bethe Ansatz
results with an overall good agreement for high temperatures and a
discrepancy for low temperatures simply due to the different size
of the charge gap [22]. The charge
susceptibility has been also computed as a function of the
filling. The peculiar behavior we found (i.e., the double peak
structure, the large renormalization of the charge fluctuations as
the system approaches the metal-insulator transition and the
vanishing at exactly half-filling) well reproduce the results
found by the finite temperature Bethe Ansatz technique
[28,29]. Namely, we find that the
system overcomes a non-trivial metal-insulator transition in the
sense that the charge susceptibility is largely enhanced in the
vicinity of half-filling
[21,22]. These results show that the method is a
reasonable framework to study the one-dimensional Hubbard model.