XXZ-type Bethe ansatz equations and quasi-polynomials

TL;DR

This paper establishes a correspondence between solutions of Bethe ansatz equations for XXZ-type models and collections of quasi-polynomials, extending previous results for XXX-type models and Gaudin models.

Contribution

It introduces a novel correspondence between Bethe ansatz solutions and quasi-polynomials for XXZ-type models, generalizing earlier work on related models.

Findings

Extended the correspondence to XXZ-type models

Connected Bethe solutions with quasi-polynomials

Generalized previous results for XXX-type models

Abstract

We study solutions of the Bethe ansatz equation for the XXZ-type integrable model associated with the Lie algebra sl_N. We give a correspondence between solutions of the Bethe ansatz equations and collections of quasi-polynomials. This extends the results of E.Mukhin and A.Varchenko for the XXX-type model and the trigonometric Gaudin model.