Efeitos topológicos na teoria do líquido de Fermi

Abstract

The study of strongly correlated systems is a big challenge for theoretical physics. Such analysis gives us a better understanding of important collective phenomena, which are manifest in a variety of applications and in novel theoretical speculations. This work describes in a introductory way some of this phenomena. In particular, it investigates how the topological effects of the Hilbert spaces associated to quantum systems interfere with their properties. In the first chapter we will discuss the basical aspects of interacting fermionic systems, on the context of the Fermi liquid theory. Later, we will develop the concept of topological phases making use of basic quantum mechanics principles. Finally, we will connect the two theories together to begin a construction of a topological Fermi liquid theory, which can be used to explain some experimental results. We conclude giving a highlight of possible future works in the field.