Deformed Calogero-Sutherland model and fractional Quantum Hall effect
Deformed Calogero-Sutherland model and fractional Quantum Hall effect
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DOI：
10.1063/1.4973509
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发表时间：
2016-03
期刊：
影响因子：
--
通讯作者：
F. Atai;E. Langmann
中科院分区：
文献类型：
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作者：
F. Atai;E. Langmann
变形的Calogero-Sutherland（CS）模型是一个含有任意数量两类粒子的量子可积系统，在特殊情况下可退化为标准CS模型。我们发现，一个已知的集体场描述的CS模型，这是基于共形场理论（CFT），实际上是一个集体场描述的变形CS模型。这提供了变形CS模型在温氏分数量子霍尔效应（Fractional Quantum Hall Effect，简称FHE）的有效场论中的自然应用，其中两种粒子对应于电子和准空穴激发。特别是，我们使用有关超级杰克多项式的已知数学结果来获得由货车埃尔堡和斯考滕斯在FQHE背景下提出的标准正交CFT基的简单显式公式。
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.