Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Improved bounds on the spectral gap above frustration free ground states
  of quantum spin chains
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int