Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lieb-Schultz-Mattis theorem in higher dimensions from approximate
  magnetic translation symmetry   We prove the Lieb-Schultz-Mattis (LSM) theorem on the energy spectrum of a
general two or three-dimensional quantum many-body system with the U(1)
particle number conservation and translation symmetry. Especially, it is
demonstrated that the theorem holds in a system with long-range interactions.
To this end, we introduce approximate magnetic translation symmetry under the
total magnetic flux $\Phi=2\pi$ instead of the exact translation symmetry, and
explicitly construct low energy variational states. The energy spectrum at
$\Phi=2\pi$ is shown to agree with that at $\Phi=0$ in the thermodynamic limit,
which concludes the LSM theorem.

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The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
2
The categories of this paper are: math