The Bulk-Edge Correspondence for Disordered Chiral Chains

  title={The Bulk-Edge Correspondence for Disordered Chiral Chains},
  author={Gian Michele Graf and Jacob Shapiro},
  journal={Communications in Mathematical Physics},
We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given Hamiltonian with nearest neighbor hopping the two indices are equal. We also give a new formulation of the index in terms of the Lyapunov exponents of the zero energy Schrödinger equation, which illustrates the conditions for a… 

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