Fases geométricas e emaranhamento em sistemas quânticos de spins

Abstract

Geometric phases are associated with the description of many phenomena in quantum mechanics. The aim of this thesis is to analyze geometric phases in quantum spin chains and relate their behavior to the entanglement dynamics of the system. In this context, we discuss how to determine geometric phases acquired by Heisenberg chains in the presence of magnetic fields, showing that the contribuition of the interaction to the geometric phase is connected with the average entanglement exhibited by an initially separable state of the chain during its evolution in Hilbert space, where we consider the global entanglement as a measure of nonseparability. This relationship promotes the interaction geometric phase as an indicator of the entanglement available in the system, which may constitute a useful tool to quantum tasks based on entanglement as a resource to their performance.