Open Collections

Abstract

In this thesis we study two different one dimensional systems. The first project is on the transverse dynamical structure factors of the XXZ spin chain and the second project is on magnetism of zigzag edges of graphene nano-ribbons. In chapter 2, we apply field theory methods, first developed to study x-ray edge singularities, to interacting one-dimensional systems in order to include band curvature effects and study edge singularities at arbitrary momentum. We point out that spin chains with uniform Dzyaloshinskii-Moriya interactions provide an opportunity to test these theories since these interactions may be exactly eliminated by a gauge transformation that shifts the momentum. However, this requires an extension of these x-ray edge methods to the transverse spectral function of the XXZ spin chain in a magnetic field. In chapter 3, by considering the Hubbard model in the weak coupling limit, U