Calogero-Moser models with noncommutative spin interactions

TL;DR

This paper introduces integrable elliptic Calogero-Sutherland-Moser models with noncommutative spin interactions, generalizing existing models by incorporating modular functions that reduce global spin symmetry.

Contribution

It constructs new integrable models with noncommutative spin interactions, extending the class of Calogero-Moser models and recovering known models as special cases.

Findings

Models include noncommutative spin interactions with modular function potentials

Global spin symmetry is generally broken to U(1) phase symmetries

Previously known models are special cases of the new construction

Abstract

We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the global spin symmetry of the model down to a product of U(1) phase symmetries. Previously known models are recovered as special cases.