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. https://resolver.caltech.edu/CaltechAUTHORS:20141112-123606275

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Abstract

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:

URL	URL Type	Description
https://doi.org/10.1007/JHEP12(2015)052	DOI	Article
https://link.springer.com/article/10.1007%2FJHEP12%282015%29052	Publisher	Article
http://arxiv.org/abs/1406.7329	arXiv	Discussion Paper

ORCID:

Author	ORCID
Kapustin, Anton	0000-0003-3903-5158
Thorngren, Ryan	0000-0001-9433-3399
Turzillo, Alex	0000-0003-4293-4293
Wang, Zitao	0000-0002-2326-2674

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

Funders:

Funding Agency	Grant Number
Department of Energy (DOE)	DE-FG02-92ER40701
SCOAP3	UNSPECIFIED

Subject Keywords:

Topological Field Theories, Effective field theories, Topological States of Matter

Other Numbering System:

Other Numbering System Name	Other Numbering System ID
CALT-TH	2014-163

Issue or Number:

DOI:

10.1007/JHEP12(2015)052

Record Number:

CaltechAUTHORS:20141112-123606275

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20141112-123606275

Official Citation:

Kapustin, A., Thorngren, R., Turzillo, A. et al. J. High Energ. Phys. (2015) 2015: 1. https://doi.org/10.1007/JHEP12(2015)052

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

51661

Collection:

CaltechAUTHORS

Deposited By:

Joy Painter

Deposited On:

12 Nov 2014 21:28

Last Modified:

10 Nov 2021 19:14

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