Published October 20, 2016
| Submitted + Published
Journal Article
Open
Spin TQFTs and fermionic phases of matter
- Creators
- Gaiotto, Davide
- Kapustin, Anton
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.
Additional Information
© 2016 World Scientific Publishing Company. Published 19 October 2016. We thank Z. Gu and D. Freed for helpful discussions and J. Morgan for educating one of us (AK) about spin structures and cobordism. The research of DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of AK was supported in part by the DOE grant DE-FG02-92ER40701 and by the Simons Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.Attached Files
Published - s0217751x16450445.pdf
Submitted - 1505.05856.pdf
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1505.05856.pdf
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Additional details
- Eprint ID
- 66640
- Resolver ID
- CaltechAUTHORS:20160504-095915162
- Perimeter Institute for Theoretical Physics
- Industry Canada
- Ontario Ministry of Economic Development and Innovation
- DE-FG02-92ER40701
- Department of Energy (DOE)
- Simons Foundation
- Created
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2016-05-04Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field