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Interacting anyons in topological quantum liquids: The golden chain

Adrian Feiguin·Simon Trebst·Andreas W. W. Ludwig·Matthias Troyer·Alexei Kitaev·Zhenghan Wang·Michael H. Freedman
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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 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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Adrian Feiguin, Simon Trebst, Andreas W. W. Ludwig, Matthias Troyer, Alexei Kitaev, Zhenghan Wang, Michael H. Freedman. 2006-12-13. Interacting anyons in topological quantum liquids: The golden chain. https://doi.org/10.1103/physrevlett.98.160409

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