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Spin TQFTs and fermionic phases of matter

Gaiotto, Davide and Kapustin, Anton (2016) Spin TQFTs and fermionic phases of matter. International Journal of Modern Physics A, 31 (28-29). Art. No. 1645044. ISSN 0217-751X. https://resolver.caltech.edu/CaltechAUTHORS:20160504-095915162

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1142/S0217751X16450445DOIArticle
http://www.worldscientific.com/doi/abs/10.1142/S0217751X16450445PublisherArticle
http://arxiv.org/abs/1505.05856arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
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.
Funders:
Funding AgencyGrant Number
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Department of Energy (DOE)DE-FG02-92ER40701
Simons FoundationUNSPECIFIED
Issue or Number:28-29
Record Number:CaltechAUTHORS:20160504-095915162
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160504-095915162
Official Citation:Spin TQFTs and fermionic phases of matter Davide Gaiotto and Anton Kapustin International Journal of Modern Physics A 2016 31:28n29
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66640
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 May 2016 20:22
Last Modified:03 Oct 2019 09:58

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