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Fractonic order in infinite-component Chern-Simons gauge theories

Ma, Xiuqi and Shirley, Wilbur and Cheng, Meng and Levin, Michael and McGreevy, John and Chen, Xie (2022) Fractonic order in infinite-component Chern-Simons gauge theories. Physical Review B, 105 (19). Art. No. 195124. ISSN 2469-9950. doi:10.1103/PhysRevB.105.195124.

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Fracton order features point excitations that either cannot move at all or are only allowed to move in a lower-dimensional submanifold of the whole system. In this paper, we generalize the (2+1)-dimensional [(2+1)D] U(1) Chern-Simons (CS) theory, a powerful tool in the study of (2+1)D topological orders, to include infinite gauge field components and find that they can describe interesting types of (3+1)-dimensional fracton order beyond what is known from exactly solvable models and tensor gauge theories. On the one hand, they can describe foliated fractonic systems for which increasing the system size requires insertion of nontrivial (2+1)D topological states. The CS formulation provides an easier approach to study the phase relation among foliated models. More interestingly, we find simple examples that lie beyond the foliation framework, characterized by 2D excitations of infinite order and irrational braiding statistics. This finding extends our realm of understanding of possible fracton phenomena.

Item Type:Article
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URLURL TypeDescription Paper
Ma, Xiuqi0000-0001-8294-2277
Levin, Michael0000-0002-5765-6591
McGreevy, John0000-0002-7077-1041
Additional Information:© 2022 American Physical Society. Received 6 March 2021; revised 28 March 2022; accepted 20 April 2022; published 18 May 2022. We are indebted to inspiring discussions with R. Mong, T. Zhang, X.-G. Wen, Y.-M. Lu, Z. Wang, and K. Slagle. We also thank P.-S. Hsin for pointing out that a fermionic Abelian topological order can always be decomposed into a bosonic Abelian topological order and transparent fermions. X.M, W.S., and X.C. are supported by the National Science Foundation under Award No. DMR-1654340, the Simons collaboration on “Ultra-Quantum Matter,” and the Institute for Quantum Information and Matter at Caltech. X.C. is also supported by the Walter Burke Institute for Theoretical Physics at Caltech. M.C. is supported by NSF CAREER (Grant No. DMR-1846109) and the Alfred P. Sloan foundation. This work was supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative research agreement Grant No. DE-SC0009919, by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (Grant No. 651440, X.C., M.L., J.M., X.M., W.S.).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation651440
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0009919
Issue or Number:19
Record Number:CaltechAUTHORS:20210106-102305508
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107336
Deposited By: George Porter
Deposited On:06 Jan 2021 22:40
Last Modified:03 Jun 2022 21:21

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