Microscopic models of interacting Yang–Lee anyons
Microscopic models of interacting Yang–Lee anyons
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杨-李任意子相互作用的微观模型
DOI：
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发表时间：
2010
期刊：
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通讯作者：
M. Troyer
中科院分区：
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作者：
E. Ardonne;J. Gukelberger;A. Ludwig;S. Trebst;M. Troyer
相互作用的非阿贝尔任意子的集体态最近主要是在某些分数量子霍尔态的背景下进行研究的，例如在填充分数ν=5/2时提出的描述量子霍尔高原物理的Moore-Read态。在本文中，我们进一步扩展了这一研究方向，并提出了相互作用任意子模型的非幺正推广。特别地，我们引入了Yang-Lee任意子的概念，讨论了它们与所谓的“加夫年”量子霍尔波函数的关系，并描述了它们相互作用的基本模型。该模型的一维（1D）版本-原始金链模型的非酉推广-可以通过精确代数解和数值对角化来完全理解。讨论了一般su(2)k任意子理论及其伽罗瓦共轭的链模型的无间隙理论。我们进一步引入并求解了非幺正Yang-Lee任意子的一维Levin-Wen模型。
Collective states of interacting non-Abelian anyons have recently been studied mostly in the context of certain fractional quantum Hall states, such as the Moore–Read state proposed to describe the physics of the quantum Hall plateau at filling fraction ν=5/2. In this paper, we further expand this line of research and present non-unitary generalizations of interacting anyon models. In particular, we introduce the notion of Yang–Lee anyons, discuss their relation to the so-called ‘Gaffnian’ quantum Hall wave function and describe an elementary model for their interactions. A one-dimensional (1D) version of this model—a non-unitary generalization of the original golden chain model—can be fully understood in terms of an exact algebraic solution and numerical diagonalization. We discuss the gapless theories of these chain models for general su(2)k anyonic theories and their Galois conjugates. We further introduce and solve a 1D version of the Levin–Wen model for non-unitary Yang–Lee anyons.