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Collective States of Interacting Fibonacci Anyons

Trebst, Simon and Ardonne, Eddy and Feiguin, Adrian and Huse, David A. and Ludwig, Andreas W. W. and Troyer, Matthias (2008) Collective States of Interacting Fibonacci Anyons. Physical Review Letters, 101 (5). Art. No. 050401. ISSN 0031-9007. doi:10.1103/PhysRevLett.101.050401.

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We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry end points we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.

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Additional Information:©2008 The American Physical Society. (Received 4 February 2008; published 30 July 2008). We acknowledge insightful discussions with N. Bonesteel, M. Freedman, A. Kitaev, M. Levin, and Z. Wang. Our numerical simulations were based on the ALPS libraries [18]. D.A.H. thanks NSF Nos. DMR-0213706 and PHY-0551164 for support. A.W.W.L. was supported, in part, by NSF No. DMR-0706140.
Funding AgencyGrant Number
National Science FoundationDMR-0213706
National Science FoundationPHY-0551164
National Science FoundationDMR-0706140
Issue or Number:5
Record Number:CaltechAUTHORS:TREprl08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11331
Deposited By: Archive Administrator
Deposited On:02 Aug 2008 04:05
Last Modified:08 Nov 2021 21:57

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