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By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, weinvestigate the trigonometric SU(3) model with generic open boundaries. Theeigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Qrelation, and the corresponding eigenstates are expressed in terms of nestedBethe-type eigenstates which have well-defined homogeneous limit. This exactsolution provides a basis for further analyzing the thermodynamic propertiesand correlation functions of the anisotropic models associated with higher rankalgebras.

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries