Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimensional evolution between one- and two-dimensional topological
  phases   Dimensional evolution between one- ($1D$) and two-dimensional ($2D$)
topological phases is investigated systematically. The crossover from a $2D$
topological insulator to its $1D$ limit shows oscillating behavior between a
$1D$ ordinary insulator and a $1D$ topological insulator. By constructing a
$2D$ topological system from a $1D$ topological insulator, it is shown that
there exist possibly weak topological phases in $2D$ time-reversal invariant
band insulators, one of which can be realized in anisotropic systems. The
topological invariant of the phase is $Z_{2}=0$. However the edge states may
appear along specific boundaries. It can be interpreted as arranged $1D$
topological phases, and have symmetry-protecting nature as the corresponding
$1D$ topological phase. Robust edge states can exist under specific conditions.
These results provide further understanding on $2D$ time-reversal invariant
insulators, and can be realized experimentally.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an