# On the Bethe states of the one-dimensional supersymmetric t-J model with generic open boundaries

## TL;DR

This paper presents an exact solution for the supersymmetric t-J model with open boundaries using algebraic and off-diagonal Bethe ansatz, enabling analysis of its thermodynamic properties.

## Contribution

It combines algebraic and off-diagonal Bethe ansatz methods to solve the supersymmetric t-J model with open boundaries, providing explicit eigenvalues and eigenstates.

## Key findings

- Eigenvalues expressed via inhomogeneous T-Q relation
- Eigenstates as nested Bethe states with homogeneous limit
- Foundation for analyzing thermodynamics and correlations

## Abstract

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t-J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe states which have well-defined homogeneous limit. This exact solution provides basis for further analyzing the thermodynamic properties and correlation functions of the model.