Gapless Edge-Modes and Topology in the Qi-Wu-Zhang Model: A Real-Space Analysis

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.
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