Fermionic Symmetry Protected Topological Phases and Cobordisms

2014/06/30 by Anton Kapustin, Ryan Thorngren, Alex Turzillo +1 · 2 citations
Physics and Astronomy · #cond-mat.str-el #hep-th

paper · pdf · doi:10.1007/jhep12(2015)052

published as JHEP 1512:052,2015 · 26 pages, new references added and a new section on decorated domain walls in v2

arxiv created 2015/08/18 · arxiv updated 2016/02/09

Abstract

It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic SPT phases with Z/2 symmetry, where Z/2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimension less than or equal to 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.

Cited by

• Fermionic Villain model with exact lattice chiral symmetries
• Exploring two dimensional ℤ₂ invariant phases with time reversal symmetry and their transitions with topological operations

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