Algebraic properties of an integrable t-J model with impurities

TL;DR

This paper explores the algebraic structure of an integrable t-J model with impurities, presenting Bethe ansatz equations for different gradings and establishing the supersymmetry properties of the states.

Contribution

It introduces three forms of Bethe ansatz equations for the model and proves the highest weight property of the states under the supersymmetry algebra.

Findings

Bethe ansatz equations for three gradings are derived

Bethe states are highest weight vectors of gl(2|1)

Complete set of states constructed using supersymmetry generators

Abstract

We investigate the algebraic structure of a recently proposed integrable $t-J$ model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz states are highest weight vectors of the underlying $gl(2|1)$ supersymmetry algebra. By acting with the $gl(2|1)$ generators we construct a complete set of states for the model.