A note on the Bethe ansatz solution of the supersymmetric t-J model

TL;DR

This paper provides a simplified proof demonstrating the equivalence of three Bethe ansatz equation sets for the supersymmetric t-J model, confirming that their transfer matrix eigenvalues are consistent.

Contribution

It introduces a new, simplified proof of the equivalence of Bethe ansatz equations for the supersymmetric t-J model using polynomial properties.

Findings

The three Bethe ansatz equation sets are equivalent.

Transfer matrix eigenvalues are consistent across the different sets.

The proof simplifies understanding of the model's integrability.

Abstract

The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain polynomials. We also show that the corresponding transfer matrix eigenvalues agree.