Drinfeld twists and algebraic Bethe ansatz of the supersymmetric model associated with $U_q(gl(m|n))$

TL;DR

This paper constructs Drinfeld twists for a supersymmetric quantum algebra, enabling symmetric representations of creation operators, and explicitly derives Bethe vectors for the $U_q(gl(2|1))$ model, advancing algebraic Bethe ansatz techniques.

Contribution

It introduces explicit Drinfeld twists for $U_q(gl(m|n))$ and derives symmetric creation operators and Bethe vectors for the supersymmetric model.

Findings

Explicit Drinfeld twists for $U_q(gl(m|n))$ constructed.

Symmetric representations of creation operators obtained.

Bethe vectors explicitly expressed for the $U_q(gl(2|1))$ model.

Abstract

We construct the Drinfeld twists (or factorizing $F$-matrices) of the supersymmetric model associated with quantum superalgebra $U_q(gl(m|n))$, and obtain the completely symmetric representations of the creation operators of the model in the $F$-basis provided by the $F$-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the $F$-basis for the $U_q(gl(2|1))$-model (the quantum t-J model).