Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum phase transition from the topological viewpoint   This study targets quantum phases which are characterized by topological
properties and no associated with the symmetry breaking. We concern ourselves
primarily with the transitions among these quantum phases. This type of quantum
phase transition was investigated by $G$-cobordism in unified framework. This
framework provides a useful method to investigate a new quantum phase.

8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg