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Fracton Models on General Three-Dimensional Manifolds

Shirley, Wilbur and Slagle, Kevin and Wang, Zhenghan and Chen, Xie (2018) Fracton Models on General Three-Dimensional Manifolds. Physical Review X, 8 (3). Art. No. 031051. ISSN 2160-3308. http://resolver.caltech.edu/CaltechAUTHORS:20180829-095556028

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Abstract

Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some “topological” features: They support fractional bulk excitations (dubbed fractons) and a ground-state degeneracy that is robust to local perturbations. However, because previous fracton models have been defined and analyzed only on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground-state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physrevx.8.031051DOIArticle
https://arxiv.org/abs/1712.05892arXivDiscussion Paper
ORCID:
AuthorORCID
Slagle, Kevin0000-0002-8036-3447
Wang, Zhenghan 0000-0002-5253-6400
Additional Information:© 2018 the Author(s). 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 5 February 2018; revised manuscript received 28 May 2018; published 29 August 2018) We are indebted to Michael Freedman, Ni Yi, Michael Pretko, Burak Şahinoğlu, and Yong Baek Kim for inspiring discussions. We also thank the Kavli Institute for Theoretical Physics where some of the discussion took place. This research is supported in part by the National Science Foundation under Grant No. NSF PHY-1125915. W. S. and X. C. are supported by the National Science Foundation under Grant No. DMR-1654340, the Alfred P. Sloan Research Fellowship, the Walter Burke Institute for Theoretical Physics, and the Institute for Quantum Information and Matter. K. S. is supported by the NSERC of Canada and the Center for Quantum Materials at the University of Toronto. Z. W. is supported by the National Science Foundation under Grant No. DMR-1411212.
Group:Institute for Quantum Information and Matter, IQIM, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFPHY-1125915
NSFDMR-1654340
Alfred P. Sloan FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
University of TorontoUNSPECIFIED
NSFDMR-1411212
Record Number:CaltechAUTHORS:20180829-095556028
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180829-095556028
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89271
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:29 Aug 2018 17:52
Last Modified:29 Aug 2018 17:52

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