Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Criticality in the Chiral-Symmetric AIII Class at Strong
  Disorder   The chiral AIII symmetry class in the periodic table of topological
insulators contains topological phases classified by a winding number $\nu$ for
each odd space-dimension. An open problem for this class is the
characterization of the phases and phase-boundaries in the presence of strong
disorder. In this work, we derive a covariant real-space formula for $\nu$ and,
using an explicit 1-dimensional disordered topological model, we show that
$\nu$ remains quantized and non-fluctuating when disorder is turned on, even
though the bulk energy-spectrum is completely localized. Furthermore, $\nu$
remains robust even after the insulating gap is filled with localized states,
but when the disorder is increased even further, an abrupt change of $\nu$ to a
trivial value is observed. Using exact analytic calculations, we show that this
marks a critical point where the localization length diverges. As such, in the
presence of disorder, the AIII class displays a markedly different physics from
everything known to date, with robust invariants being carried entirely by
localized states and bulk extended states emerging from an absolutely localized
spectrum. Detailed maps and a clear physical description of the phases and
phase boundaries are presented based on numerical and exact analytic
calculations.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn