Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model

TL;DR

This paper investigates integrable Kondo impurities in the one-dimensional t-J model using boundary graded quantum inverse scattering and algebraic Bethe ansatz, deriving reflection matrices and Bethe equations.

Contribution

It introduces new boundary K matrices based on reflection equation algebras for the t-J model with impurities and solves the models exactly.

Findings

Derived explicit boundary K matrices for impurity interactions.

Solved the models using algebraic Bethe ansatz.

Obtained Bethe ansatz equations for the impurity systems.

Abstract

Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.