The two-dimensional Hubbard model in the Hartree-Fock approximation

Abstract

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. We consider that for these students it is very important to have texts that analyze pedagogically the theoretical research methods of the subject. We show how to determine the thermodynamic properties of the Hubbard model for the two-dimensional square lattice, utilizing the Hartree-Fock approximation. All the procedures and peculiarities which lead to the determination of the thermodynamic properties and to the comprehension of the meaning of the Hartree-Fock approximation applied to models of strongly correlated electron systems are pedagogically presented in detail. We obtain the magnetization, the magnetic susceptibility, the internal energy, the specific heat, and also a magnetic phase diagram of the studied system. Our approach clearly shows that the use of the Hartree-Fock approximation, in this case, is very simple.