# From algebraic to coordinate Bethe ansatz for square ice

## TL;DR

This paper bridges the algebraic and coordinate Bethe ansatz methods for the square ice model, providing detailed constructions and proofs to unify these approaches in integrable systems.

## Contribution

It offers a detailed exposition connecting algebraic and coordinate Bethe ansatz for the six vertex model, including proofs of key formulas and their equivalence.

## Key findings

- Established the connection between algebraic and coordinate Bethe ansatz for square ice.
- Proved formulas of V.E. Korepin for eigenvectors of the transfer matrix.
- Unified the two Bethe ansatz approaches in the context of the six vertex model.

## Abstract

In this text, we provide a detailed exposition of the Algebraic Bethe ansatz for square ice (or six vertex model), which allows the construction of candidate eigenvectors for the transfer matrices of this model. We also prove some formula of V.E. Korepin for these vectors, which leads to an identification, up to a non-zero complex factor, with the vector obtained by coordinate Bethe ansatz.