Interacting anyons in topological quantum liquids: The golden chain

Details Interacting anyons in topological quantum liquids: The golden chain Interacting anyons in topological quantum liquids: The golden chain

2006-12-13

arxiv.org/abs/cond-mat/0612341v1

Phys. Rev. Lett. 98, 160409 (2007).

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.98.160409

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 conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the two-dimensional tricritical Ising model is given using the restricted-solid-on-solid (RSOS) representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.

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