The Bulk-Edge Correspondence for Disordered Chiral Chains

Gian Michele Graf, Jacob Shapiro

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 topological phase transition occurring in the mobility gap regime.

Original languageEnglish (US)
Pages (from-to)829-846
Number of pages18
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Nov 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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