Calculation of thermodynamic properties of the Hubbard model using perturbation theory

Abstract

Magnetic systems of strongly correlated electrons are present in many technologically relevant materials. Models of these systems have been studied using many theoretical approaches. The perturbation theory has been used successfully in one-dimensional systems. In this paper, we extend the perturbation theory developed by Beni and Pincus, originally applied to one-dimensional lattices, for lattices with different geometries. We calculate the specific heat and the magnetic susceptibility of the Hubbard model for the square, ladder and one-dimensional dimerized lattices. Our results, within the limits of validity of the parameters used to perform the perturbative approach, are consistent with those available in the literature, obtained by other techniques. Furthermore, we show that our approach to perturbation theory is feasible to be applied to various other types of lattice, including three-dimensional. We conclude that in the form given in this work, the perturbation theory becomes an important tool for investigating the thermodynamic properties of magnetic systems of strongly correlated electrons.