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Fracton topological order via coupled layers

Ma, Han and Lake, Ethan and Chen, Xie and Hermele, Michael (2017) Fracton topological order via coupled layers. Physical Review B, 95 (24). Art. No. 245126. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20170622-102731134

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Abstract

In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial dimensions. These topological phases have subextensive topological ground-state degeneracy and possess excitations whose movement is restricted in interesting ways. Our coupled layer approach is used to construct several different fracton topological phases, both from stacked layers of simple d=2 topological phases and from stacks of d=3 fracton topological phases. This perspective allows us to shed light on the physics of the X-cube model recently introduced by Vijay, Haah, and Fu, which we demonstrate can be obtained as the strong-coupling limit of a coupled three-dimensional stack of toric codes. We also construct two new models of fracton topological order: a semionic generalization of the X-cube model, and a model obtained by coupling together four interpenetrating X-cube models, which we dub the ‘four color cube model”. The couplings considered lead to fracton topological orders via mechanisms we dub “p-string condensation” and “p-membrane condensation”, in which strings or membranes built from particle excitations are driven to condense. This allows the fusion properties, braiding statistics, and ground-state degeneracy of the phases we construct to be easily studied in terms of more familiar degrees of freedom. Our work raises the possibility of studying fracton topological phases from within the framework of topological quantum field theory, which may be useful for obtaining a more complete understanding of such phases.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.95.245126DOIArticle
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.245126PublisherArticle
https://arxiv.org/abs/1701.00747arXivDiscussion Paper
Additional Information:© 2017 American Physical Society. Received 20 January 2017; revised manuscript received 15 May 2017; published 21 June 2017. X.C. would like to thank A. Kubica and J. Mozgunov for discussion. H.M. would like to thank Y.-M. Lu and Z. Bi for insightful discussion. M.H. and H.M. were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences (BES) under Award No. DE-SC0014415. X.C. is supported by the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics. E.L. was supported by the NSF Grant No. PHY-1560023. Some of this work was carried out at the Kavli Institute for Theoretical Physics, which is supported by the National Science Foundation under Grant No. NSF PHY11-25915.
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
NSFPHY-1560023
NSFPHY11-25915
Record Number:CaltechAUTHORS:20170622-102731134
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170622-102731134
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78464
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Jun 2017 17:34
Last Modified:22 Jun 2017 17:34

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