Deformed Calogero-Sutherland model and fractional Quantum Hall effect

TL;DR

This paper links the deformed Calogero-Sutherland model to the fractional quantum Hall effect, providing a conformal field theory description and explicit formulas for basis states relevant to electron and quasi-hole excitations.

Contribution

It demonstrates that the deformed CS model can be described by conformal field theory and applies this to the FQHE, deriving explicit formulas for the orthonormal basis using super Jack polynomials.

Findings

CFT description of the deformed CS model established

Explicit formulas for orthonormal basis derived

Application to FQHE with electron and quasi-hole excitations

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.