Completeness of the Bethe ansatz for the six and eight-vertex models

TL;DR

This paper addresses longstanding issues in the Bethe ansatz for six- and eight-vertex models, demonstrating that the coordinate Bethe ansatz provides a complete set of states by resolving key difficulties.

Contribution

It proves the completeness of the coordinate Bethe ansatz for these models, overcoming known problems such as 'beyond the equator' and string solutions.

Findings

Bethe ansatz is complete for six- and eight-vertex models

Key difficulties in the Bethe ansatz are resolved

Theoretical confirmation of the Bethe ansatz's completeness

Abstract

We discuss some of the difficulties that have been mentioned in the literature in connection with the Bethe ansatz for the six-vertex model and XXZ chain, and for the eight-vertex model. In particular we discuss the ``beyond the equator'', infinite momenta and exact complete string problems. We show how they can be overcome and conclude that the coordinate Bethe ansatz does indeed give a complete set of states, as expected.