Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Gaps and Incompressibility in a $ \nu = 1/3 $ Fractional
  Quantum Hall System   We study an effective Hamiltonian for the standard $\nu=1/3$ fractional
quantum Hall system in the thin cylinder regime. We give a complete description
of its ground state space in terms of what we call Fragmented Matrix Product
States, which are labeled by a certain family of tilings of the one-dimensional
lattice. We then prove that the model has a spectral gap above the ground
states for a range of coupling constants that includes physical values. As a
consequence of the gap we establish the incompressibility of the fractional
quantum Hall states. We also show that all the ground states labeled by a
tiling have a finite correlation length, for which we give an upper bound. We
demonstrate by example, however, that not all superpositions of tiling states
have exponential decay of correlations.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph