Emery vs. Hubbard model for cuprate superconductors: A composite operator method study

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 superconductors. 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 qualitatively 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.