The bulk-edge correspondence for disordered chiral chains. (English) Zbl 1401.82031
Summary: 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.
MSC:
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
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