Topology of Entanglement in Multipartite States with Translational Invariance

The topology of entanglement in multipartite states with translational invariance is discussed in this article. Two global features are foundby which one can distinguish distinct states. These are the cyclic unit and the quantised geometric phase. Furthermore the topology is indicated by the fractional spin. Finally a scheme is presented for preparation of these types of states in spin chain systems, in which the degeneracy of the energy levels characterises the robustness of the states with translational invariance.