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Interacting anyons in topological quantum liquids: The golden chain

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arxiv cond-mat/0612341 v1 pith:WS2RCV6F submitted 2006-12-13 cond-mat.str-el quant-ph

Adrian Feiguin , Simon Trebst , Andreas W. W. Ludwig , Matthias Troyer , Alexei Kitaev , Zhenghan Wang , Michael H. Freedman This is my paper · ORCID
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keywords anyonschainmodelquantumanyoniccriticalinteractingneighboring
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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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