Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of quantum critical states of integrable
  antiferromagnetic spin chains and their correspondent two-dimensional
  topological phases   We examine the effective field theory of the Bethe ansatz integrable
Heisenberg antiferromagnetic spin chains. It shows that the quantum critical
theories for the integer spin-S chains should be characterized by the
SO(3)level-S Wess-Zumino-Witten model, and classified by the third cohomology
group $H^{3}(SO(3),Z)=Z$. Depending on the parity of spin S, this integer
classification is further divided into two distinct universality classes, which
are associated with two completely different conformal field theories: the
even-S chains have gapless bosonic excitations and the odd-S chains have both
bosonic and fermionic excitations. We further show that these two classes of
critical states correspond to the boundary states of two distinct topological
phases in two dimension, which can be described by two-dimensional doubled
SO(3) topological Chern-Simons theory and topological spin theory,
respectively.

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The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th