Topology versus Anderson localization: Nonperturbative solutions in one dimension

Alexander Altland, Dmitry Bagrets, Alex Kamenev

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23 Scopus citations

Abstract

We present an analytic theory of quantum criticality in quasi-one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters (g,χ) representing localization and topological properties, respectively. Certain critical values of χ (half-integer for Z classes, or zero for Z2 classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two-parameter flow of the integer quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given in terms of the transfer-matrix solution of corresponding supersymmetric nonlinear sigma models. In Z2 classes we uncover a hidden supersymmetry, present at the quantum critical point.

Original languageEnglish (US)
Article number085429
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number8
DOIs
StatePublished - Feb 27 2015

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