Estudo do modelo de Hubbard estendido : o caso do dímero de Mott - Juliano, Raffael Chaves (2014)
Compounds based on transition metals such as vanadium dioxide (VO2), present under certain conditions metal-insulator transitions. Regarding to VO2, this transition is accompanied by a change in its cristalline structure through dimerization of two vanadium atoms on di erent sites. Here, it is this bound state between two vanadium atoms that emerges the idea of a Mott's dimer. In this work, using exact diagonalization, we study the Hubbard model in its extended version exploring the physics of Mott's dimer. We obtain explicitly all eigenvalues and eigenvectors of this model. Varying the model parameters, we explore the energy dependence of all eigenvalues of the system. We also performed an analysis of the total electron occupation and the charge compressibility (density of states) as a function of chemical potential. In order to better understand the physical properties of a two-site Hubbard model, we study the behavior of the double occupancy, the total energy and the speci c heat as a function of temperature and the Coulomb interaction parameters. Moreover, various physical quantities (double occupancy, internal energy, speci c heat, entropy, magnetization and magnetic susceptibility) of dimer's Mott were calculated analytically using the method of the canonical ensemble.