Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient Conditions for Topological Order in Insulators   We prove the existence of low energy excitations in insulating systems at
general filling factor under certain conditions, and discuss in which cases
these may be identified as topological excitations. This proof is based on
previously proven locality results. In the case of half-filling it provides a
significantly shortened proof of the recent higher dimensional
Lieb-Schultz-Mattis theorem.

28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
2
The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg