Deformed Calogero-Sutherland model and fractional Quantum Hall effect

Abstract

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.

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Cited by in corpus (8)

• Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems
• Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operators
• Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• Exact wave functions and entropies of the one dimensional Regularized Calogero model
• Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation
• Conformal field theory, solitons, and elliptic Calogero--Sutherland models
• From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators