Generalized Calogero-Sutherland systems from many-matrix models

TL;DR

This paper generalizes Calogero-Sutherland systems by reducing many-matrix models, resulting in integrable particles with internal degrees of freedom and complex interactions, with explicit spectrum and wavefunctions derived.

Contribution

It introduces a new class of integrable many-particle systems with internal degrees of freedom from matrix model reductions, extending previous models.

Findings

Systems are integrable with explicitly derived spectrum

Wavefunctions of the quantum systems are obtained

Internal degrees of freedom involve SU(M) non-invariant interactions

Abstract

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a model involving many unitary matrices. The resulting systems consist of particles on the circle with internal degrees of freedom, coupled through modifications of the inverse-square potential. The coupling involves SU(M) non-invariant (anti)ferromagnetic interactions of the internal degrees of freedom. The systems are shown to be integrable and the spectrum and wavefunctions of the quantum version are derived.