title: Interacting anyons in topological quantum liquids: the golden chain.
abstract: We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.
authors.affiliation: Microsoft Research, Station Q, University of California, Santa Barbara, California 93106, USA.
authors.forename: Adrian
authors.initials: A
authors.lastname: Feiguin
authors.forename: Simon
authors.initials: S
authors.lastname: Trebst
authors.forename: Andreas W W
authors.initials: AW
authors.lastname: Ludwig
authors.forename: Matthias
authors.initials: M
authors.lastname: Troyer
authors.forename: Alexei
authors.initials: A
authors.lastname: Kitaev
authors.forename: Zhenghan
authors.initials: Z
authors.lastname: Wang
authors.forename: Michael H
authors.initials: MH
authors.lastname: Freedman