Quantum toroidal gl(1) and Bethe ansatz

TL;DR

This paper develops a Bethe ansatz method for a quantum toroidal gl(1) model, utilizing shuffle realizations and module quotients, potentially applicable to various integrable models.

Contribution

It introduces a novel Bethe ansatz approach for quantum toroidal gl(1) models using shuffle realizations and module quotients, expanding the toolkit for integrable systems.

Findings

Bethe ansatz method established for quantum toroidal gl(1) model.

Hamiltonian derived from a multiplication operator via quotient.

Approach potentially applicable to a wide class of models.

Abstract

We establish the method of Bethe ansatz for the XXZ type model obtained from the R-matrix associated to quantum toroidal gl(1). We do that by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models.