A short introduction to Fibonacci anyon models

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dc.creatorTrebst, Simon
dc.creatorTroyer, Matthias
dc.creatorWang, Zhenghan
dc.creatorLudwig, Andreas W. W.
dc.date2009-02-19
dc.date.accessioned2026-07-07T12:44:06Z
dc.date.available2026-07-07T12:44:06Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0902.3275
dc.identifierhttp://arxiv.org/abs/0902.3275
dc.identifierProg. Theor. Phys. Supp. 176, 384 (2008)
dc.identifierdoi:10.1143/PTPS.176.384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220654
dc.subjectStatistical Mechanics
dc.subjectMesoscale and Nanoscale Physics
dc.subjectStrongly Correlated Electrons
dc.titleA short introduction to Fibonacci anyon models
dc.typetext

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