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Deformed Calogero-Sutherland model and fractional quantum Hall effect. (English) Zbl 1355.81188
Summary: 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.
©2017 American Institute of Physics

MSC:
81V70 Many-body theory; quantum Hall effect
81R12 Groups and algebras in quantum theory and relations with integrable systems
81T45 Topological field theories in quantum mechanics
14D15 Formal methods and deformations in algebraic geometry
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