Wilson Loop and Berry Phases in the 2D Lattice Models

In the given Master thesis we considered a 2D-lattice. For computing the Wilson loop we used the non-Abelian stokes theorem. This theorem appeared advantageous for simplifying the computations after showing the main feature of the curvature tensor defined in the Brillouin Zone. For the system under consideration we sorted the different topological states by computing the Berry phases and assigned the corresponding topological invariants to them. For this we considered a somewhat general as well as the specific parametrization of the quantities characterizing the system.