Abstract
In this paper, we construct a Hamiltonian of the impurity model with next-nearest-neighbor interaction within the framework of the open boundary Heisenberg XYZ spin chain. This impurity model is an exactly solved one and it degenerates to the integrable XXZ impurity model under the triangular limit. It is the first approach to add the impurities and next-nearest-neighbor interaction to the integrable completely anisotropic Heisenberg spin chain. We find also that the impurity parameters in the bulk are real when the cross parameter is imaginary for the Hermitian Hamiltonian, or vice versa, when the next-nearest-neighbor interaction is introduced. The eigenvalue of the Hamiltonian and the Bethe ansatz equations for the trigonometric limit case are derived also.
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