Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A theorem regarding families of topologically non-trivial fermionic
  systems   We introduce a Hamiltonian for fermions on a lattice and prove a theorem
regarding its topological properties. We identify the topological criterion as
a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian
polynomial). The topological invariant is not only the first Chern number, but
also the sign of the Pfaffian polynomial coming from a notion of duality. Such
Hamiltonian can describe non-trivial Chern insulators, single band
superconductors or multiorbital superconductors. The topological features of
these families are completely determined as a consequence of our theorem. Some
specific model examples are explicitly worked out, with the computation of
different possible topological invariants.

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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: q-alg
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio