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Fermionic Symmetry Protected Topological Phases and Cobordisms

Kapustin, Anton and Thorngren, Ryan and Turzillo, Alex and Wang, Zitao (2015) Fermionic Symmetry Protected Topological Phases and Cobordisms. Journal of High Energy Physics, 2015 (12). Art. No. 052. ISSN 1126-6708. doi:10.1007/JHEP12(2015)052.

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It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with Z_2 symmetry, where Z_2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Thorngren, Ryan0000-0001-9433-3399
Turzillo, Alex0000-0003-4293-4293
Wang, Zitao0000-0002-2326-2674
Additional Information:© 2015 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: August 18, 2015; Accepted: November 25, 2015; Published: December 10, 2015. R.T. would like to thank Xie Chen for patiently answering his questions and Rob Kirby for an enlightening discussion. A. K. would like to acknowledge conversations with Alexei Kitaev and Zhengcheng Gu. The work of A.K., A.T., and Z.W. was supported in part DOE grant DE-FG02-92ER40701.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-92ER40701
Subject Keywords:Topological Field Theories, Effective field theories, Topological States of Matter
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Other Numbering System NameOther Numbering System ID
Issue or Number:12
Record Number:CaltechAUTHORS:20141112-123606275
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Official Citation:Kapustin, A., Thorngren, R., Turzillo, A. et al. J. High Energ. Phys. (2015) 2015: 1.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51661
Deposited By: Joy Painter
Deposited On:12 Nov 2014 21:28
Last Modified:10 Nov 2021 19:14

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