SSH MODEL — 1D TOPOLOGICAL INSULATOR

Su-Schrieffer-Heeger chain: bulk topology and protected edge states

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The Su-Schrieffer-Heeger (SSH) model is the simplest 1D topological insulator. A chain of dimers alternates between intra-cell hopping v and inter-cell hopping w. When w > v, the winding number of the Bloch Hamiltonian is 1 (topological phase), producing zero-energy edge states exponentially localized at the chain ends. When v > w, the winding number is 0 (trivial phase) and the gap is featureless. The edge states are topologically protected — they persist against any perturbation that respects chiral symmetry, a profound consequence of the bulk-boundary correspondence.