Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional quantum Hall effect in the Hofstadter model of interacting
  fermions   Applying a unified approach, we study integer quantum Hall effect (IQHE) and
fractional quantum Hall effect (FQHE) in the Hofstadter model with short range
interaction between fermions. An effective field, that takes into account the
interaction, is determined by both the amplitude and phase. Its amplitude is
proportional to the interaction strength, the phase corresponds to the minimum
energy. In fact the problem is reduced to the Harper equation with two
different scales: the first is a magnetic scale (cell size corresponding to a
unit quantum magnetic flux), the second scale (determines the inhomogeneity of
the effective field) forms the steady fine structure of the Hofstadter spectrum
and leads to the realization of fractional quantum Hall states. In a sample of
finite sizes with open boundary conditions, the fine structure of the
Hofstadter spectrum also includes the fine structure of the edge chiral modes.
The subbands in a fine structure of the Hofstadter band (HB) are separated
extremely small quasigaps. The Chern number of a topological HB is conserved
during the formation of its fine structure. Edge modes are formed into HB, they
connect the nearest-neighbor subbands and determine the fractional conductance
for the fractional filling at the Fermi energies corresponding to these
quasigaps.

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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg