Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting and identifying 2D symmetry-protected topological,
  symmetry-breaking and intrinsic topological phases with modular matrices via
  tensor-network methods   Symmetry-protected topological (SPT) phases exhibit nontrivial order if
symmetry is respected but are adiabatically connected to the trivial product
phase if symmetry is not respected. However, unlike the symmetry-breaking
phase, there is no local order parameter for SPT phases. Here we employ a
tensor-network method to compute the topological invariants characterized by
the simulated modular $S$ and $T$ matrices to study transitions in a few
families of two-dimensional (2D) wavefunctions which are $\mathbb{Z}_N$ ($N=2\,
\&3$) symmetric. We find that in addition to the topologically ordered phases,
the modular matrices can be used to identify nontrivial SPT phases and detect
transitions between different SPT phases as well as between symmetric and
symmetry-breaking phases. Therefore, modular matrices can be used to
characterize various types of gapped phases in a unifying way.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph