A Short Introduction to Fibonacci Anyon Models(Interaction and Nanostructural Effects in Low-Dimensional Systems)

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概要

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• 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)_κ statistics. The κ→∞ limit of the latter yields ordinary SU(2) spin chains.

• 2009-02-05

著者

• TREBST Simon

  Microsoft Research, Station Q, University of California

• TROYER Matthias

  Theoretische Physik, ETH Zurich

• WANG Zhenghan

  Microsoft Research, Station Q, University of California

• LUDWIG Andreas

  Physics Department, University of California

• Trebst Simon

  Microsoft Research Station Q University Of California

• Wang Zhenghan

  Microsoft Research Station Q University Of California

• Ludwig Andreas

  Physics Department University Of California

• Troyer Matthias

  Theoretische Physik Eidgenossische Technische Hochschule Zurich

• Troyer Matthias

  Theoretische Physik Eth Zurich

関連論文

• A Short Introduction to Fibonacci Anyon Models(Interaction and Nanostructural Effects in Low-Dimensional Systems)
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• A Nonmagnetic Impurity in a Quantum Critical Spin System
• Static and Dynamic Holes in a Quantum Critical Antiferromagnet

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