A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models

TL;DR

This paper investigates the integrability of non-Hermitian, PT-symmetric extensions of Calogero models across various Lie algebras and potential types, confirming their integrability with necessary modifications.

Contribution

It extends the analysis of PT-symmetric Calogero models to all Lie algebras and potential types, demonstrating their integrability with added terms for non-rational cases.

Findings

All extended models remain integrable.

Additional terms are needed for non-rational potentials.

Extensions are valid beyond rational models.

Abstract

We consider non-Hermitian but PT-symmetric extensions of Calogero models, which have been proposed by Basu-Mallick and Kundu for two types of Lie algebras. We address the question of whether these extensions are meaningful for all remaining Lie algebras (Coxeter groups) and if in addition one may extend the models beyond the rational case to trigonometric, hyperbolic and elliptic models. We find that all these new models remain integrable, albeit for the non-rational potentials one requires additional terms in the extension in order to compensate for the breaking of integrability.