Complete set of commuting observables for a two-site Hubbard model

The aim of this paper is to present an exact solution of the Hubbard model in a simplified case. Considering the simplest problem of a two-site entity, a solution of the model is obtained by using a suitable complete set of commuting observables. Owing to this approach, we show that some features of the physics of insulating and metallic systems may be understood within a simple unified picture. Furthermore, we are confident that this purely quantum mechanical approach turns out to be of particular interest for a general reader and undergraduate or graduate physics students.