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.
@article{arxiv.0801.4602,
title = {Collective states of interacting Fibonacci anyons},
author = {Simon Trebst and Eddy Ardonne and Adrian Feiguin and David A. Huse and Andreas W. W. Ludwig and Matthias Troyer},
journal= {arXiv preprint arXiv:0801.4602},
year = {2008}
}