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Assembling Fibonacci anyons from a ℤ_3 parafermion lattice model

Stoudenmire, E. M. and Clarke, David J. and Mong, Roger S. K. and Alicea, Jason (2015) Assembling Fibonacci anyons from a ℤ_3 parafermion lattice model. Physical Review B, 91 (23). Art. No. 235112. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20150625-130152181

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Abstract

Recent concrete proposals suggest it is possible to engineer a two-dimensional bulk phase supporting non-Abelian Fibonacci anyons out of Abelian fractional quantum Hall systems. The low-energy degrees of freedom of such setups can be modeled as ℤ_3 parafermions “hopping” on a two-dimensional lattice. We use the density matrix renormalization group to study a model of this type interpolating between the decoupled-chain, triangular-lattice, and square-lattice limits. The results show clear evidence of the Fibonacci phase over a wide region of the phase diagram, most notably including the isotropic triangular-lattice point. We also study the broader phase diagram of this model and show that elsewhere it supports an Abelian state with semionic excitations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.91.235112DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.235112PublisherArticle
http://arxiv.org/abs/1501.05305arXivDiscussion Paper
Additional Information:© 2015 American Physical Society. Received 9 March 2015; revised manuscript received 28 April 2015; published 8 June 2015. We would like to acknowledge helpful discussions with L. Cincio, J. Carrasquilla, P. Fendley, T. Hughes, and A. Gorshkov. Simulations were performed on the Perimeter Institute HPC. We are grateful for generous support from the Sherman Fairchild Foundation (R.M.), the National Science Foundation through Grant No. DMR-1341822 (J.A.); the Alfred P. Sloan Foundation (J.A.); the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250; and the Walter Burke Institute for Theoretical Physics at Caltech.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSFDMR-1341822
Alfred P. Sloan FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics FrontiersUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Walter Burke Institute for Theoretical PhysicsUNSPECIFIED
Classification Code:PACS: 75.40.Mg
Record Number:CaltechAUTHORS:20150625-130152181
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150625-130152181
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58613
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Jun 2015 21:19
Last Modified:25 Jun 2015 21:19

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