斐波那契任意子模型简介
A short introduction to Fibonacci anyon models
摘要：
我们讨论了如何通过将量子自旋Hamilton推广到任意子自由度来构建相互作用任意子的模型。最简单的相互作用在能量上有利于任意子对融合到平凡（“身份”）通道中，类似于量子海森堡模型有利于自旋对形成自旋单线态。我们介绍了任意子的理论，并详细讨论了如何基集和矩阵表示的相互作用项可以获得，使用非阿贝尔斐波那契任意子为例。除了讨论“黄金链”，一个一维系统的任意子与最近邻相互作用，我们还提出了更复杂的相互作用项的推导，如三个任意子相互作用的精神的Majumdar-Ghosh自旋链，更长的范围内的相互作用和两条腿的梯子。我们还讨论了具有一般非阿贝尔su（2）_k统计量的任意子的推广。后者的k到无穷大极限产生普通的SU（2）自旋链。
英文摘要：
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.
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