Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian
  Fractionally Filled Topological Insulators   The energy and entanglement spectrum of fractionally filled interacting
topological insulators exhibit a peculiar manifold of low energy states
separated by a gap from a high energy set of spurious states. In the current
manuscript, we show that in the case of fractionally filled Chern insulators,
the topological information of the many-body state developing in the system
resides in this low-energy manifold. We identify an emergent many-body
translational symmetry which allows us to separate the states in
quasi-degenerate center of mass momentum sectors. Within one center of mass
sector, the states can be further classified as eigenstates of an emergent (in
the thermodynamic limit) set of many-body relative translation operators. We
analytically establish a mapping between the two-dimensional Brillouin zone for
the Fractional Quantum Hall effect on the torus and the one for the fractional
Chern insulator. We show that the counting of quasi-degenerate levels below the
gap for the Fractional Chern Insulator should arise from a folding of the
states in the Fractional Quantum Hall system at identical filling factor. We
show how to count and separate the excitations of the Laughlin, Moore-Read and
Read-Rezayi series in the Fractional Quantum Hall effect into two-dimensional
Brillouin zone momentum sectors, and then how to map these into the momentum
sectors of the Fractional Chern Insulator. We numerically check our results by
showing the emergent symmetry at work for Laughlin, Moore-Read and Read-Rezayi
states on the checkerboard model of a Chern insulator, thereby also showing, as
a proof of principle, that non-Abelian Fractional Chern Insulators exist.

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The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con