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Symmetry protected topological phases and generalized cohomology

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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Correspondence to Davide Gaiotto.

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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