Estudo das correlações eletrônicas no modelo de Hubbard de uma banda ferromagnético - Chaura, Julián Alberto Faúndez (2018)
This work is focused on the study of strongly correlated electron systems, which have an infinite spatial dimension d → ∞. The strongly correlated electron system is characterized by the presence of strong Coulomb interaction, which does not allow perturbative treatment in contrast to other degrees freedom in the system. Hence, these are truly many-body systems and in most cases it is necessary to use numerical techniques as well as analytical tools to perform this type of study. In many types of electron systems there might be interactions that could lead to a complete collapse of the metalic state of the system. The most important case of study is the Mott insulating phase. One of the models that allows the study of electrons correlation effects is the Hubbard model, which in spite of its simple form it provides a good description of electron correlations in crystalline lattices. The Hubbard Hamiltonian is composed by one kinetic energy term (the hopping t term), which allows to describe the motion of electrons and a Coulomb repulsion term between electrons. In this study we apply a perturbation in the kinetic energy term, which allows to obtain the one-particle Green’s function from a perturbation around the atomic limit, to describe the properties of the Hubbard model. In infinite spatial dimension limit the local Green’s function can be mapped on the Anderson impurity model subject to a self-consistent condition with the lattice Green’s function. Using this approach it is possible to study the correlation between electrons which is maped from a manybody system to a local problem. The lattice used in this work is the Lieb lattice. Our objective is to explain and understand electronic interactions effects in itinerant ferromagnetic systems. We will consider a spin channel with a metalic band and a strongly polarized channel. We study the effects of many-particle interactions in the minority and majority spin channels due to the presence of strong electronic interactions. As a result, we show the formation of local moments in the minority spin channel and the presence of weak electronic localization for the majority carriers.