Author(s):

Authors: Alexander Altland, Dmitry Bagrets, Alex Kamenev

We present an analytic theory of quantum criticality in quasi one-dimensional

topological Anderson insulators. We describe these systems in terms of two

parameters $(g,\chi)$ representing localization and topological properties,

respectively. Certain critical values of $\chi$ (half-integer for $\Bbb{Z}$

classes, or zero for $\Bbb{Z}_2$ 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 non-linear

sigma-models. In $\Bbb{Z}_2$ classes we uncover a hidden supersymmetry, present

at the quantum critical point.

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