The open XXZ spin chain model and the topological basis realization
In this paper, it is shown that the Hamiltonian of the open spin-1 XXZ chain model can be constructed from the generators of the Birman–Murakami–Wenzl (B–M–W) algebra. Without the topological parameter d (describing the unknotted loop [Formula: see text] in topology) reducing to a fixed value, the topological basis states can be connected with the open XXZ spin chain. Then some particular properties of the topological basis states in this system have been investigated. We find that the topological basis states are the three eigenstates of a four-spin-1 XXZ chain model without boundary term. Specifically, all the spin single states of the system fall on the topological basis subspace. And the number of the spin single states of the system is equal to that of the topological basis states.