Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bott periodicity for $Z_2$ symmetric ground states of gapped
  free-fermion systems   Building on the symmetry classification of disordered fermions, we give a
proof of the proposal by Kitaev, and others, for a "Bott clock" topological
classification of free-fermion ground states of gapped systems with symmetries.
Our approach differs from previous ones in that (i) we work in the standard
framework of Hermitian quantum mechanics over the complex numbers, (ii) we
directly formulate a mathematical model for ground states rather than
spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools
rather than K-theory. Key to our proof is a natural transformation that squares
to the standard Bott map and relates the ground state of a d-dimensional system
in symmetry class s to the ground state of a (d+1)-dimensional system in
symmetry class s+1. This relation gives a new vantage point on topological
insulators and superconductors.

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The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas