  Within the Composite Operator Method (COM), we report the solution of the
Emery model (also known as p-d or three band model), which is relevant for the
cuprate high-Tc superconduc- tors. We also discuss the relevance of the
often-neglected direct oxygen-oxygen hopping for a more accurate, sometimes
unique, description of this class of materials. The benchmark of the solution
is performed by comparing our results with the available quantum Monte Carlo
ones. Both single- particle and thermodynamic properties of the model are
studied in detail. Our solution features a metal-insulator transition at half
filling. The resulting metal-insulator phase diagram agrees qual- itatively
very well with the one obtained within Dynamical Mean-Field Theory. We discuss
the type of transition (Mott-Hubbard (MH) or charge-transfer (CT)) for the
microscopic (ab-initio) parameter range relevant for cuprates getting, as
expected a CT type. The emerging single-particle scenario clearly suggests a
very close relation between the relevant sub-bands of the three- (Emery) and
the single- band (Hubbard) models, thus providing an independent and
non-perturbative proof of the validity of the mapping between the two models
for the model parameters optimal to describe cuprates. Such a result confirms
the emergence of the Zhang-Rice scenario, which has been recently questioned.
We also report the behavior of the specific heat and of the entropy as
functions of the temperature on varying the model parameters as these
quantities, more than any other, depend on and, consequently, reveal the most
relevant energy scales of the system.
