Asymmetric 6-vertex model and classical Ruijsenaars-Schneider system of particles

TL;DR

This paper explores the connection between quantum integrable models solved by Bethe ansatz, specifically the asymmetric 6-vertex model, and classical Calogero-type integrable systems, highlighting their mathematical correspondence.

Contribution

It establishes a detailed correspondence between the inhomogeneous asymmetric 6-vertex model and the classical Ruijsenaars-Schneider system of particles.

Findings

Demonstrates the Bethe ansatz solution for the asymmetric 6-vertex model.

Shows the classical-quantum correspondence with the Ruijsenaars-Schneider system.

Provides a framework for understanding integrable models through this correspondence.

Abstract

We discuss the correspondence between models solved by Bethe ansatz and classical integrable systems of Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric 6-vertex model parametrized by trigonometric (hyperbolic) functions.