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Interacting Anyons in Topological Quantum Liquids: The Golden Chain

Feiguin, Adrian and Trebst, Simon and Ludwig, Andreas W. W. and Troyer, Matthis and Kitaev, Alexei and Wang, Zhenghan and Freedman, Michael H. (2007) Interacting Anyons in Topological Quantum Liquids: The Golden Chain. Physical Review Letters, 98 (16). Art. No. 160409. ISSN 0031-9007. doi:10.1103/PhysRevLett.98.160409.

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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 (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.

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Wang, Zhenghan0000-0002-5253-6400
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.
Issue or Number:16
Record Number:CaltechAUTHORS:FEIprl07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8566
Deposited By: Archive Administrator
Deposited On:20 Aug 2007
Last Modified:08 Nov 2021 20:51

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