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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 (2020) Fractonic order in infinite-component Chern-Simons gauge theories. . (Unpublished)

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2+1D multi-component U(1) gauge theories with a Chern-Simons (CS) term provide a simple and complete characterization of 2+1D Abelian topological orders. In this paper, we extend the theory by taking the number of component gauge fields to infinity and find that they can describe interesting types of 3+1D "fractonic" order. "Fractonic" describes the peculiar phenomena that point excitations in certain strongly interacting systems either cannot move at all or are only allowed to move in a lower dimensional sub-manifold. In the simplest cases of infinite-component CS gauge theory, different components do not couple to each other and the theory describes a decoupled stack of 2+1D fractional Quantum Hall systems with quasi-particles moving only in 2D planes -- hence a fractonic system. We find that when the component gauge fields do couple through the CS term, more varieties of fractonic orders are possible. For example, they may describe foliated fractonic systems for which increasing the system size requires insertion of nontrivial 2+1D topological states. Moreover, we find examples which lie beyond the foliation framework, characterized by 2D excitations of infinite order and braiding statistics that are not strictly local.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Levin, Michael0000-0002-5765-6591
McGreevy, John0000-0002-7077-1041
Additional Information:We are indebted to inspiring discussions with Tina Zhang, Xiao-Gang Wen, Yuan-Ming Lu, Zhenghan Wang, and Kevin Slagle. We also thank Po-Shen 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 number 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 (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 DE-SC0009919, by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, XC, ML, JM, XM, WS).
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
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:06 Jan 2021 22:40

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