Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Quantum Critical Phase and Lifshitz Transition in an Extended Periodic
  Anderson Model
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin