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.
Additional Information
© 2007 The American Physical Society (Received 19 December 2006; published 20 April 2007) We thank E. Ardonne, N. Bonesteel, P. Fendley, C. Nayak, G. Refael, S. H. Simon, and J. Slingerland for discussions.Attached Files
Published - FEIprl07.pdf
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- Eprint ID
- 8566
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- CaltechAUTHORS:FEIprl07
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2007-08-20Created from EPrint's datestamp field
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2021-11-08Created from EPrint's last_modified field