Topology of Entanglement in Multipartite States with Translational Invariance

TL;DR

This paper explores the topological properties of entanglement in translationally invariant multipartite states, identifying key features like cyclic units, geometric phases, and fractional spin, and proposes a scheme for their preparation in spin chains.

Contribution

It introduces a novel topological framework for understanding entanglement in translationally invariant states and presents a method for preparing such states in spin chain systems.

Findings

Distinct states are characterized by cyclic units and quantized geometric phases.

Fractional spin indicates the topology of entanglement.

Degeneracy of energy levels relates to state robustness.

Abstract

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.