title: Collective states of interacting Fibonacci anyons.
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 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.
authors.affiliation: Microsoft Research, Station Q, University of California-Santa Barbara, CA 93106, USA.
authors.forename: Simon
authors.initials: S
authors.lastname: Trebst
authors.forename: Eddy
authors.initials: E
authors.lastname: Ardonne
authors.forename: Adrian
authors.initials: A
authors.lastname: Feiguin
authors.forename: David A
authors.initials: DA
authors.lastname: Huse
authors.forename: Andreas W W
authors.initials: AW
authors.lastname: Ludwig
authors.forename: Matthias
authors.initials: M
authors.lastname: Troyer