Assembling Fibonacci anyons from a ℤ_3 parafermion lattice model
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.
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.Attached Files
Published - PhysRevB.91.235112.pdf
Submitted - 1501.05305.pdf
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Additional details
- Eprint ID
- 58613
- Resolver ID
- CaltechAUTHORS:20150625-130152181
- Sherman Fairchild Foundation
- DMR-1341822
- NSF
- Alfred P. Sloan Foundation
- Institute for Quantum Information and Matter (IQIM)
- GBMF1250
- Gordon and Betty Moore Foundation
- Walter Burke Institute for Theoretical Physics
- Created
-
2015-06-25Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics