QFT and BeyondNo Access

Spin TQFTs and fermionic phases of matter

Davide Gaiotto

Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5, Canada

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and

Anton Kapustin

Simons Center for Geometry and Physics, Stony Brook, NY 11790, USA

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https://doi.org/10.1142/S0217751X16450445Cited by:137 (Source: Crossref)

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.

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