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Within the Composite Operator Method (COM), we report the solution of theEmery model (also known as p-d or three band model), which is relevant for thecuprate high-Tc superconduc- tors. We also discuss the relevance of theoften-neglected direct oxygen-oxygen hopping for a more accurate, sometimesunique, description of this class of materials. The benchmark of the solutionis performed by comparing our results with the available quantum Monte Carloones. Both single- particle and thermodynamic properties of the model arestudied in detail. Our solution features a metal-insulator transition at halffilling. The resulting metal-insulator phase diagram agrees qual- itativelyvery well with the one obtained within Dynamical Mean-Field Theory. We discussthe type of transition (Mott-Hubbard (MH) or charge-transfer (CT)) for themicroscopic (ab-initio) parameter range relevant for cuprates getting, asexpected a CT type. The emerging single-particle scenario clearly suggests avery close relation between the relevant sub-bands of the three- (Emery) andthe single- band (Hubbard) models, thus providing an independent andnon-perturbative proof of the validity of the mapping between the two modelsfor the model parameters optimal to describe cuprates. Such a result confirmsthe emergence of the Zhang-Rice scenario, which has been recently questioned.We also report the behavior of the specific heat and of the entropy asfunctions of the temperature on varying the model parameters as thesequantities, more than any other, depend on and, consequently, reveal the mostrelevant energy scales of the system.

Emery vs. Hubbard model for cuprate superconductors: a Composite Operator Method study