Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Competing exotic quantum phases of spin-$1/2$ ultra-cold lattice bosons
  with extended spin interactions
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg