Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of fractional quantum Hall states with spatial symmetries   Fractional quantum Hall (FQH) states are examples of symmetry-enriched
topological states (SETs): in addition to the intrinsic topological order,
which is robust to symmetry breaking, they possess symmetry-protected
topological invariants, such as fractional charge of anyons and fractional Hall
conductivity. In this paper we develop a comprehensive theory of
symmetry-protected topological invariants for FQH states with spatial
symmetries, which applies to Abelian and non-Abelian topological states, by
using a recently developed framework of $G$-crossed braided tensor categories
($G\times$BTCs) for SETs. We consider systems with $U(1)$ charge conservation,
magnetic translational, and spatial rotational symmetries, in the continuum and
for all $5$ orientation-preserving crystalline space groups in two dimensions,
allowing arbitrary rational magnetic flux per unit cell, and assuming that
symmetries do not permute anyons. In the crystalline setting, applicable to
fractional Chern insulators and spin liquids, symmetry fractionalization is
fully characterized by a generalization to non-Abelian states of the charge,
spin, discrete torsion, and area vectors, which specify fractional charge,
angular momentum, linear momentum, and fractionalization of the translation
algebra for each anyon. The topological response theory contains $9$ terms,
which attach charge, linear momentum, and angular momentum to magnetic flux,
lattice dislocations, disclinations, corners, and units of area. Using the
$G\times$BTC formalism, we derive the formula relating charge filling to the
Hall conductivity and flux per unit cell; in the continuum this relates the
filling fraction and the Hall conductivity without assuming Galilean
invariance. We provide systematic formulas for topological invariants within
the $G\times$BTC framework; this gives, for example, a new categorical
definition of the Hall conductivity.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph