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arXiv 0902.0998cond-mat.mes-hallcond-mat.stat-mech
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边界共形场论与非阿贝尔拓扑态边准粒子的隧穿

Boundary Conformal Field Theory and Tunneling of Edge Quasiparticles in non-Abelian Topological States

Paul Fendley, Matthew P. A. Fisher, Chetan Nayak

摘要:

我们解释如何(扰动)边界共形场论使我们能够理解隧道的边缘准粒子在非阿贝尔拓扑状态。大块非阿贝尔准粒子和边缘之间的耦合是由于共振隧穿到准粒子上的零模,这导致零模与边缘杂交。这可以重新表述为从一个保形不变的边界条件到另一个在相关的临界统计力学模型的流动。在点接触处从一个边缘到另一个边缘的平移可以将系统部分或完全一分为二。这可以在临界统计力学模型中重新表述为从一种类型的缺陷线到另一种类型的缺陷线的流动。我们在nu=5/2量子霍尔态和临界伊辛模型的背景下详细说明了这两种现象。我们简要地讨论了斐波那契任意子的情况下,并通过解释一般的配方和它的物理解释结束。

英文摘要:

We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant tunneling to a zero mode on the quasiparticle, which causes the zero mode to hybridize with the edge. This can be reformulated as the flow from one conformally-invariant boundary condition to another in an associated critical statistical mechanical model. Tunneling from one edge to another at a point contact can split the system in two, either partially or completely. This can be reformulated in the critical statistical mechanical model as the flow from one type of defect line to another. We illustrate these two phenomena in detail in the context of the nu=5/2 quantum Hall state and the critical Ising model. We briefly discuss the case of Fibonacci anyons and conclude by explaining the general formulation and its physical interpretation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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