The topological basis realization and the corresponding Heisenberg model of spin-1 chain

Abstract

In this paper, it is shown that the Heisenberg model of spin-1 chain can be constructed from the Birman---Wenzl algebra generator while we have got that the Heisenberg model of spin-$$\frac{1}{2}$$12 chain can be constructed from the Temperley---Lieb algebra generator in our previous work (Sun et al. in EPL 94:50001, 2011). Here, we investigate the topological space, we find that the number of topological basis states raise from the previous two to three, and they are also the three eigenstates of a closed four-qubit Heisenberg model of spin-1 chain. Specifically, all the topological basis states are also the spin single states and one of them is the energy single state of the system. It is worth noting that all conclusions we get in this paper are consistent with our previous work (Sun et al. in EPL 94:50001, 2011). These just indicate that the topological basis states have particular properties in the system.