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Symmetry Protected Topological phases and Generalized Cohomology
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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.
Forward citations
Cited by 2 Pith papers
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Bosonic SPT and invertible phases and its relation to Steenrod's problem
Bosonic beyond-cohomology SPT phases are governed by a mod-3 Steenrod-power differential, and a new 6+1-dimensional Z3×Z3 Dijkgraaf-Witten phase is nontrivial on simplicial complexes but trivial on manifolds.
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Anomaly-free symmetries with obstructions to gauging and onsiteability
A new class of two-dimensional lattice symmetries is anomaly-free yet obstructs both gauging and on-site realization, with the obstruction classified by H^2(G,Q+).
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