Exact diagonalization of the generalized supersymmetric t-J model with boundaries

TL;DR

This paper provides an exact solution for the eigenvalues and Bethe ansatz equations of the generalized supersymmetric t-J model with boundaries, using the graded quantum inverse scattering method across three gradings.

Contribution

It introduces a comprehensive method to solve the supersymmetric t-J model with boundaries in multiple gradings, expanding the analytical tools available for such models.

Findings

Derived eigenvalues for the model with boundaries.

Formulated Bethe ansatz equations for three gradings.

Enhanced understanding of boundary effects in supersymmetric models.

Abstract

We study the generalized supersymmetric $t-J$ model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric $t-J$ model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t-J$ model with boundaries in three different backgrounds.