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Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order

Burnell, F. J. and Chen, Xie and Fidkowski, L. and Vishwanath, Ashvin (2014) Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order. Physical Review B, 90 (24). Art. No. 245122. ISSN 1098-0121. https://resolver.caltech.edu/CaltechAUTHORS:20150115-095144828

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Abstract

We construct an exactly soluble Hamiltonian on the D=3 cubic lattice, whose ground state is a topological phase of bosons protected by time-reversal symmetry, i.e., a symmetry-protected topological (SPT) phase. In this model, excitations with anyonic statistics are shown to exist at the surface but not in the bulk. The statistics of these surface anyons is explicitly computed and shown to be identical to the three-fermion Z2 model, a variant of Z2 topological order which cannot be realized in a purely D=2 system with time-reversal symmetry. Thus the model realizes a novel surface termination for three-dimensional (3D) SPT phases, that of a fully symmetric gapped surface with topological order. The 3D phase found here was previously proposed from a field theoretic analysis but is outside the group cohomology classification that appears to capture all SPT phases in lower dimensions. Such phases may potentially be realized in spin-orbit-coupled magnetic insulators, which evade magnetic ordering. Our construction utilizes the Walker-Wang prescription to create a 3D confined phase with surface anyons, which can be extended to other topological phases.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.90.245122DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.245122PublisherArticle
http://arxiv.org/abs/1302.7072arXivDiscussion Paper
Additional Information:© 2014 American Physical Society. Received 13 July 2013; revised manuscript received 16 October 2014; published 15 December 2014. We thank P. Dumitrescu, M. P. A. Fisher, A. Kitaev, Y.-M. Lu, M. Metlitski, T. Senthil, and X.-G. Wen for helpful discussions. In particular, we thank M. P. A. Fisher for introducing us to the idea of the plumber’s nightmare geometry. A.V. is supported by ARO MURI Grant No. W911-NF-12-0461, and X.C. is supported by the Miller Institute for Basic Research in Science at Berkeley. L.F. and F.B. are grateful for the hospitality of KITP (made possible by NSF Grant No. NSF PHY11-25915). F.J.B. is supported by NSF Grant No. DMR 1352271.
Funders:
Funding AgencyGrant Number
AArmy Research Office (ARO)W911-NF-12-0461
Miller Institute for Basic Research in ScienceUNSPECIFIED
NSFPHY11-25915
NSFDMR 1352271
Issue or Number:24
Classification Code:PACS number(s): 75.10.Kt, 73.43.−f
Record Number:CaltechAUTHORS:20150115-095144828
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150115-095144828
Official Citation:Burnell, F. J., Chen, X., Fidkowski, L., & Vishwanath, A. (2014). Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order. Physical Review B, 90(24), 245122.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53765
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:15 Jan 2015 23:50
Last Modified:03 Oct 2019 07:52

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