`Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider

TL;DR

This paper establishes a correspondence between composite particles and Young tableaux, applying it to Calogero-Sutherland and Ruijsenaars-Schneider models to derive representations and connect to fractional quantum Hall states.

Contribution

It introduces a novel correspondence between composite particles and Young tableaux, enabling new representations in integrable models and fractional quantum Hall wave functions.

Findings

Derived momentum space representation of composite particles.

Obtained position space representation via bosonisation.

Constructed ground state wave functions for Jain series in fractional quantum Hall effect.

Abstract

We establish a one-to-one correspondance between the ''composite particles'' with $N$ particles and the Young tableaux with at most $N$ rows. We apply this correspondance to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we obtain a momentum space representation of the ''composite particles'' in terms of creation operators attached to the Young tableaux. Using the technique of bosonisation, we obtain a position space representation of the ''composite particles'' in terms of products of vertex operators. In the special case where the ''composite particles'' are bosons and if we add one extra quasiparticle or quasihole, we construct the ground state wave functions corresponding to the Jain series $\nu =p/(2np\pm 1) $ of the fractional quantum Hall effect.