Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology and edge states survive quantum criticality between topological
  insulators   It is often thought that emergent phenomena in topological phases of matter
are destroyed when tuning to a critical point. In particular, topologically
protected edge states supposedly delocalize when the bulk correlation length
diverges. We show that this is not true in general. Edge states of topological
insulators or superconductors remain exponentially localized---despite a
vanishing band gap---if the transition increases the topological index. This
applies to all classes where the topological classification is larger than
$Z_2$, notably including Chern insulators. Moreover, these edge states are
stable to disorder, unlike in topological semi-metals. This new phenomenon is
explained by generalizing band (or mass) inversion---a unifying perspective on
topological insulators---to kinetic inversion. In the spirit of the
bulk-boundary correspondence, we also identify topological invariants at
criticality, which take half-integer values and separate topologically-distinct
universality classes by a multi-critical point. This work enlarges the scope of
topological protection and stability by showing that bulk energy gaps can be
unnecessary. Experimental probes and stability to interactions are discussed.

0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org