Topological signatures of Multipartite Entanglement

We present a proposal to relate topological structure of worldline configurations to multipartite entanglement. Configurations result from the path-integral formulation of the density matrix in the limit of zero temperature. We consider hard-core bosons for which configurations, i.e. collections of particle paths, can be seen as geometric braids with a certain topological structure. We propose that properties of worldline configurations may realize a more comprehensive deciphering of multipartite entanglement.
By means of Monte Carlo calculations, we study checkerboard, stripe, valence-bond solids, Z₂ topologically ordered spin liquid, and superfluid phase. We find that each ground-state is characterized by a certain `topological spectrum' which can be used to differentiate among different ground-states.