Abstract
We investigate the spin-1 topological basis realization of a non-Hermitian Heisenberg XXZ chain model. For the non-Hermitian case, the Hamiltonian and the topological ground states of the system are constructed by Birman-Murakami-Wenzl algebra. The results show that all the spin singlet states belong to the topological ground states. The topological subspace and the spin singlet subspace are equivalent. The topological basis can reduce Birman-Murakami-Wenzl algebra generators, and the reduced matrices satisfy reduced Birman-Murakami-Wenzl algebra relations.
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