Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic localization of Wannier functions implies Chern triviality in
  non-periodic insulators   For gapped periodic systems (insulators), it has been established that the
insulator is topologically trivial (i.e., its Chern number is equal to $0$) if
and only if its Fermi projector admits an orthogonal basis with finite second
moment (i.e., all basis elements satisfy $\int |\boldsymbol{x}|^2
|w(\boldsymbol{x})|^2 \,\textrm{d}{\boldsymbol{x}} < \infty$). In this paper,
we extend one direction of this result to non-periodic gapped systems. In
particular, we show that the existence of an orthogonal basis with slightly
more decay ($\int |\boldsymbol{x}|^{2+\epsilon} |w(\boldsymbol{x})|^2
\,\textrm{d}{\boldsymbol{x}} < \infty$ for any $\epsilon > 0$) is a sufficient
condition to conclude that the Chern marker, the natural generalization of the
Chern number, vanishes.

10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th