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Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory

Ma, Han and Hermele, Michael and Chen, Xie (2018) Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory. Physical Review B, 98 (3). Art. No. 035111. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20180710-075128971

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Abstract

Fractons are gapped pointlike excitations in d=3 topological ordered phases whose motion is constrained. They have been discovered in several gapped models but a unifying physical mechanism for generating them is still missing. It has been noticed that in symmetric-tensor U(1) gauge theories, charges are fractons and cannot move freely due to, for example, the conservation of not only the charge but also the dipole moment. To connect these theories with fully gapped fracton models, we study Higgs and partial confinement mechanisms in rank-2 symmetric-tensor gauge theories, where charges or magnetic excitations, respectively, are condensed. Specifically, we describe two different routes from the rank-2 U(1) scalar charge theory to the X-cube fracton topological order, finding that a combination of Higgs and partial confinement mechanisms is necessary to obtain the fully gapped fracton model. On the other hand, the rank-2 Z_2 scalar charge theory, which is obtained from the former theory upon condensing charge-2 matter, is equivalent to four copies of the d=3 toric code and does not support fracton excitations. We also explain how the checkerboard fracton model can be viewed as a rank-2 Z_2 gauge theory with two different Gauss' law constraints on different lattice sites.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.98.035111DOIArticle
https://arxiv.org/abs/1802.10108arXivDiscussion Paper
Additional Information:© 2018 American Physical Society. Received 11 March 2018; revised manuscript received 5 May 2018; published 10 July 2018. H.M. thanks Michael Pretko for insightful discussion. M.H. and H.M. are supported by the US Department of Energy, Office of Science, Basic Energy Sciences (BES) under Award number DE-SC0014415. X.C. is supported by the Caltech Institute for Quantum Information and Matter, the Walter Burke Institute for Theoretical Physics, the Alfred P. Sloan research fellowship, and National Science Foundation under Award No. DMR-1654340.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0014415
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
NSFDMR-1654340
Record Number:CaltechAUTHORS:20180710-075128971
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180710-075128971
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87678
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Jul 2018 16:07
Last Modified:10 Jul 2018 16:07

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