Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 20, 2016 | Submitted + Published
Journal Article Open

Spin TQFTs and fermionic phases of matter

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

Files

1505.05856.pdf
Files (1.0 MB)
Name Size Download all
md5:f745246d093a7e83990a01c94d7c01d4
391.5 kB Preview Download
md5:3916ff44acd57ee7144818559f44e23e
655.9 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
October 18, 2023