Integrable multi-impurity open XXZ chain with next-nearest-neighbor interaction

The Hamiltonian of one-dimensional integrable multi-impurity XXZ spin chain with open boundary cases is constructed by using the method of adding para meters to the vertical matrices. This is the first approach to add multi-im purity and next-nearest-neighbor interaction to the integrable anisotropic Heisenberg spin chain. It is found that all of the impurity parameters in t he bulk must be pure imaginary numbers if the cross parameter is real for g etting the hermitian Hamiltonian, or vice versa, when the next-nearest-neig hbor interactions are introduced. The Hamiltonian can be also applied to de scribe the many body systems with two kinds of particles if all of the impu rity parameters are equal.