TY - JOUR

T1 - Topology versus Anderson localization

T2 - Nonperturbative solutions in one dimension

AU - Altland, Alexander

AU - Bagrets, Dmitry

AU - Kamenev, Alex

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/2/27

Y1 - 2015/2/27

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.91.085429

DO - 10.1103/PhysRevB.91.085429

M3 - Article

AN - SCOPUS:84924039127

SN - 1098-0121

VL - 91

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 8

M1 - 085429

ER -