A Short Introduction to Fibonacci Anyon Models

By Simon Trebst, Matthias Troyer, Zhenghan Wang, A. Ludwig. 2008

137 citations recorded by the source corpus.

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the "golden chain", a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian su(2)_k statistics. The k to infinity limit of the latter yields ordinary SU(2) spin chains.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/72baac0e8d140db3c590199ad423028db35f7c2a

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In Artificial Intelligence

  1. J. Moore
  2. Romain Vasseur

In Atomic and Molecular Physics, and Optics

  1. Romain Vasseur
  2. J. Moore
  3. B. Doyon
  4. A. Nahum
  5. Shoucheng Zhang
  6. Ashvin Vishwanath
  7. E. Witten
  8. V. Khemani

In Geometry and Topology

  1. J. Moore
  2. Romain Vasseur

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