  The topological phase transition in the Qi-Wu-Zhang model is studied using a
real-space approach. An effective Hamiltonian for the topologically protected
edge-modes in a finite-size system is developed. The topological phase
transition is understood in terms of a global perturbation to the system which
lifts the degeneracy of the edge-modes. The effective Hamiltonian method is
also applied to a one-dimensional system with spatially varying hopping
strengths to understand the impact of disorder on the edge-modes.
