Topological basis realization associated with Hermitian and non-Hermitian Heisenberg XXZ model

Abstract

We investigate the topological basis realization associated with the Hermitian and non-Hermitian Heisenberg XXZ model based on the matrix representation of the Temperley-Lieb algebra. The results show that the topological space is spanned by the topological basis associated with the Temperley-Lieb algebra. When the q-deformed parameter q is a complex number and , the corresponding model is the non-Hermitian XXZ model. The real q corresponds to the Hermitan case. The topological basis realization for these two cases is constructed by means of matrix representation of the Temperley-Lieb algebra. Then the properties of the topological basis and ground state are studied. Particularly, the four-qubit Heisenberg XXZ model is investigated in detail. We also give some discussions on the case in which q is a root of unity.