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arXiv · 0801.4602

Collective states of interacting Fibonacci anyons

Simon Trebst·Eddy Ardonne·Adrian Feiguin·David A. Huse·Andreas W. W. Ludwig·Matthias Troyer
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Abstract

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 endpoints 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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Simon Trebst, Eddy Ardonne, Adrian Feiguin, David A. Huse, Andreas W. W. Ludwig, Matthias Troyer. 2008-01-30. Collective states of interacting Fibonacci anyons. https://doi.org/10.1103/physrevlett.101.050401

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