Chern number in the Kitaev honeycomb lattice model

Abstract

We study a topological invariant in the 2D Kitaev honeycomb model: the Chern number. This model consists of a spin 1 2 hexagonal lattice that can be divided into two triangular sublattices. By applying an external perturbation we can induce a non-trivial phase for some coupling configurations that yields a non-zero Chern number. First we set a theoretical basis in order to understand the results. Then we study how different parameters affect the Chern number. More exactly; finite-size effects, an external perturbation, different coupling configurations and strengths.We will see how each of these variations change the Chern number