Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric t-J Model

TL;DR

This paper constructs Drinfeld twists for the supersymmetric t-J model, leading to symmetric representations that facilitate solving the nested Bethe ansatz and advancing understanding of its algebraic structure.

Contribution

It introduces explicit Drinfeld twists for the supersymmetric t-J model, providing a new basis that simplifies the algebraic Bethe ansatz process.

Findings

Symmetric representations of monodromy matrix achieved

Resolution of nested Bethe vectors hierarchy

Enhanced algebraic understanding of the supersymmetric t-J model

Abstract

We construct the Drinfeld twists (factorizing $F$-matrices) for the supersymmetric t-J model. Working in the basis provided by the $F$-matrix (i.e. the so-called $F$-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the $gl(2|1)$ invariant t-J model.