Collective Field Description of Spin Calogero-Sutherland Models

TL;DR

This paper uses collective field techniques to bosonize the spin Calogero-Sutherland Model, providing a new free boson representation applicable for any coupling and connecting eigenstates with Young diagrams to vertex operators.

Contribution

It introduces a bosonized Hamiltonian for the spin Calogero-Sutherland Model valid for arbitrary coupling constants, linking eigenstates to vertex operators and offering a dual Hamiltonian description.

Findings

Bosonized Hamiltonian derived for arbitrary coupling.

Eigenstates with single-row/column Young diagrams represented by vertex operators.

Dual description of the Hamiltonian constructed.

Abstract

Using the collective field technique, we give the description of the spin Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be applicable for arbitrary coupling constant and provides the bosonized Hamiltonian of the spin CSM. The boson Fock space can be identified with the Hilbert space of the spin CSM in the large $N$ limit. We show that the eigenstates corresponding to the Young diagram with a single row or column are represented by the vertex operators. We also derive a dual description of the Hamiltonian and comment on the construction of the general eigenstates.