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Phys. Rev. Lett. 101, 050401 (2008) [4 pages]

Collective States of Interacting Fibonacci Anyons

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Simon Trebst1, Eddy Ardonne2,3, Adrian Feiguin1,4, David A. Huse5, Andreas W. W. Ludwig6, and Matthias Troyer7
1Microsoft Research, Station Q, University of California, Santa Barbara, California 93106, USA
2California Institute of Technology, Pasadena, California 91125, USA
3Nordita, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
4Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
5Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
6Physics Department, University of California, Santa Barbara, California 93106, USA
7Theoretische Physik, Eidgenössische Technische Hochschule Zürich, 8093 Zürich, Switzerland

See Also: Publisher's Note

Received 4 February 2008; published 30 July 2008; corrected 23 September 2008

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.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.101.050401
DOI:
10.1103/PhysRevLett.101.050401
PACS:
05.30.Pr, 03.65.Vf, 73.43.Lp

See Also

Publisher's Note: Simon Trebst, Eddy Ardonne, Adrian Feiguin, David A. Huse, Andreas W. Ludwig, and Matthias Troyer, Publisher’s Note: Collective States of Interacting Fibonacci Anyons [Phys. Rev. Lett. 101, 050401 (2008)], Phys. Rev. Lett. 101, 149901 (2008).

 
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