The Haldane–Shastry spin chain and the topological basis realization

•We study the Haldane–Shastry model based on the topological basis realization.•Really useful effects of Yangian operators are found.•We explore some particular properties of the topological basis in these systems.•We construct a new Hamiltonian whose energy degeneracy can be changed.

In this paper, based on the topological basis states, we investigate the Hamiltonian family {H2,H3,H4}{H2,H3,H4} of a closed four-qubit Haldane–Shastry spin chain. Not only the two-qubit interaction form, but also the three-qubit interaction form and the four-qubit interaction form are presented in terms of spin operators. Meanwhile, we explore some particular properties of the topological basis states in these systems. With Yangian algebra, the symmetry of the systems and the transitions between the eigenstates have been investigated. We find a really useful effect of Y(sl(2))Y(sl(2)) operators {J±,J3}{J±,J3}, which is that they can describe the transitions between the spin single state and the spin triple states. Furthermore, we construct a new Hamiltonian, whose energy degeneracies can be changed by adjusting the strengths of the two-qubit interactions, three-qubit interactions, four-qubit interactions, and the external magnetic field.