Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization of Hall Conductance For Interacting Electrons Without
  Averaging Assumptions   We consider two-dimensional Hamiltonians on a torus with finite range, finite
strength interactions and a unique ground state with a non-vanishing spectral
gap, and a conserved local charge, as defined precisely in the text. Using the
local charge operators, we introduce a boundary magnetic flux in the horizontal
and vertical direction and evolve the ground state quasi-adiabatically around a
square of size one magnetic flux, in flux space. At the end of the evolution we
obtain a trivial Berry phase, which we compare, via a method reminiscent of
Stokes' Theorem, to the Berry phase obtained from an evolution around a small
loop near the origin. As a result, we prove, without any averaging assumption,
that the Hall conductance for interacting electron systems is quantized in
integer multiples of e^2/h up to small corrections bounded by a function that
decays as a stretched exponential in the linear size L. Finally, we discuss
extensions to the fractional case under an additional topological order
assumption to describe the multiple degenerate ground states.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics