Spin TQFTs and fermionic phases of matter

2015/05/31 by Davide Gaiotto, Anton Kapustin · 2 citations
Mathematics · Physics and Astronomy · #cond-mat.str-el #hep-th #math.QA

paper · pdf · doi:10.1142/s0217751x16450445

42 pages, 7 figures

arxiv created 2015/10/07 · arxiv updated 2016/11/23

Abstract

We study lattice constructions of gapped fermionic phases of matter. We show that the construction of fermionic Symmetry Protected Topological orders by Gu and Wen has a hidden dependence on a discrete spin structure on the Euclidean space-time. The spin structure is needed to resolve ambiguities which are otherwise present. An identical ambiguity is shown to arise in the fermionic analog of the string-net construction of 2D topological orders. We argue that the need for a spin structure is a general feature of lattice models with local fermionic degrees of freedom and is a lattice analog of the spin-statistics relation.

Cited by

• Fermionic Villain model with exact lattice chiral symmetries
• Quadratic Functions of Cocycles and Pin Structures

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