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Topological defect networks for fractons of all types

Aasen, David and Bulmash, Daniel and Prem, Abhinav and Slagle, Kevin and Williamson, Dominic J. (2020) Topological defect networks for fractons of all types. Physical Review Research, 2 (4). Art. No. 043165. ISSN 2643-1564. doi:10.1103/physrevresearch.2.043165.

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Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect TQFTs and show that topological defect networks—networks of topological defects embedded in stratified 3+1-dimensional (3+1D) TQFTs—provide a unified framework for describing various types of gapped fracton phases. In this picture, the subdimensional excitations characteristic of fractonic matter are a consequence of mobility restrictions imposed by the defect network. We conjecture that all gapped phases, including fracton phases, admit a topological defect network description and support this claim by explicitly providing such a construction for many well-known fracton models, including the X-cube and Haah's B code. To highlight the generality of our framework, we also provide a defect network construction of a fracton phase hosting non-Abelian fractons. As a byproduct of this construction, we obtain a generalized membrane-net description for fractonic ground states as well as an argument that our conjecture implies no topological fracton phases exist in 2+1-dimensional gapped systems. Our paper also sheds light on techniques for constructing higher-order gapped boundaries of 3+1D TQFTs.

Item Type:Article
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URLURL TypeDescription Paper
Aasen, David0000-0002-6552-488X
Bulmash, Daniel0000-0001-8978-4531
Prem, Abhinav0000-0003-4438-7107
Slagle, Kevin0000-0002-8036-3447
Additional Information:© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 1 May 2020; revised 29 August 2020; accepted 15 September 2020; published 30 October 2020. It is a pleasure to thank Maissam Barkeshli, Dominic Else, Jeongwan Haah, Michael Hermele, Sheng-Jie Huang, Zhu-Xi Luo, Wilbur Shirley, and Zhenghan Wang for stimulating discussions and correspondence. This paper was initiated and performed in part at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. D.A. is supported by A postdoctoral fellowship from the Gordon and Betty Moore Foundation, under the Emergent Phenomena in Quantum Systems (EPiQS) initiative, Grant No. GBMF4304. D.B. is supported by Joint Quantum Institute Physics Frontier Center at University of Maryland (JQI-PFC-UMD). A.P. acknowledges support through a Princeton Center for Theoretical Science (PCTS) fellowship at Princeton University. K.S. is supported by the Walter Burke Institute for Theoretical Physics at California Institute of Technology. D.W. acknowledges support from the Simons Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Gordon and Betty Moore FoundationGBMF4304
University of MarylandUNSPECIFIED
Princeton UniversityUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20201103-104249449
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106392
Deposited By: Tony Diaz
Deposited On:04 Nov 2020 18:20
Last Modified:16 Nov 2021 18:53

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