Symmetry Protected Topological phases and Generalized Cohomology

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. 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.

arXiv comment27 pages, 10 figures. v2: citation update

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