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Symmetry protected topological phases and generalized cohomology

Journal of High Energy Physics volume 2019, Article number: 7 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We discuss the classification of SPT phases in condensed matter systems. We review Kitaev’s argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum of gapped physical systems [20, 23]. We propose a concrete description of that spectrum and of the corresponding cohomology theory. We compare our proposal to pre-existing constructions in the literature.

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  1. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada

    Davide Gaiotto & Theo Johnson-Freyd

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  1. Davide Gaiotto
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  2. Theo Johnson-Freyd
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Correspondence to Davide Gaiotto.

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ArXiv ePrint: 1712.07950

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Gaiotto, D., Johnson-Freyd, T. Symmetry protected topological phases and generalized cohomology. J. High Energ. Phys. 2019, 7 (2019). https://doi.org/10.1007/JHEP05(2019)007

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  • DOI: https://doi.org/10.1007/JHEP05(2019)007

Keywords

  • Effective Field Theories
  • Global Symmetries
  • Topological Field Theories
  • Topological States of Matter