Journal
PHYSICAL REVIEW B
Volume 91, Issue 23, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.91.235112
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Funding
- Sherman Fairchild Foundation
- National Science Foundation [DMR-1341822]
- Alfred P. Sloan Foundation
- Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation [GBMF1250]
- Walter Burke Institute for Theoretical Physics at Caltech
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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.
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