Three-body generalization of the Sutherland model with internal degrees of freedom

TL;DR

This paper introduces a generalized spin Sutherland model with a three-body potential, analyzed using differential-difference operators derived from supersymmetric quantum mechanics and dihedral group symmetries.

Contribution

It presents a novel three-body generalization of the Sutherland model incorporating internal degrees of freedom and new commuting operators.

Findings

Development of a generalized model with three-body interactions

Use of SUSYQM supercharges and dihedral group elements in analysis

Introduction of three alternative commuting operators

Abstract

A generalized spin Sutherland model including a three-body potential is proposed. The problem is analyzed in terms of three first-order differential-difference operators, obtained by combining SUSYQM supercharges with the elements of the dihedral group~$D_6$. Three alternative commuting operators are also introduced.