Thermodynamic properties of the Hubbard model for a diatomic molecule AB

Abstract

The Hubbard model has been subject of strong interest in the condensed matter community. It is the simplest model for strongly correlated electron systems. The text books of physics are based on applications, under the form of problems, which have exact analytical solutions. Itinerant magnetic system models, for that reason, are rarely considered in text books of statistical mechanics. The students interested in the study of strongly correlated electron systems, normally, feel in the beginning of their studies a great difficulty in understanding the complex correlations of these systems. In this work, we have studied, with a pedagogical approach, the thermodynamic properties of the Hubbard model for a diatomic molecule  AB, that is, we consider a case translationally non-invariant. We apply the grand canonical ensemble method for allowing the analysis of a general situation of any average electron number per site. In the applications we consider, in particular, the case in which the average electron number per site is one. The analysis of the thermodynamic properties makes possible to conclude that the diatomic molecule AB of Hubbard exhibits ferrimagnetic behavior. Moreover, the studied system presents a conceptual and mathematical structure accessible to undergraduate students of physics in their last year, and the results show a rich variety of physics phenomena with details that make feasible a deeper comprehension of the quantum mechanisms involved in the thermodynamics properties and of the methods employed to obtain such properties.