A topological signature of multipartite entanglement

F. Lingua, W. Wang, L. Shpani, and B. Capogrosso-Sansone

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Jun 04, 2019
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Received Date: 24th May 19

Topology and entanglement promise to play a prominent role in understanding non-local properties of many-body quantum systems.Here, we present a novel proposal to relate the two and study multipartite entanglement by collecting statistics of topological invariants of hard-core bosons worldline configurations in two-dimensional lattices. We build our approach upon the path-integral formulation of the density matrix in the limit of zero temperature, and consider worldline configurations, i.e. collections of particle paths, as geometric braids with a certain topological structure. We support our proposal by studying checkerboard and stripe solids, superfluid phases, and Z2 topologically ordered phases by means of unbiased quantum Monte Carlo simulations. We find that topological invariants can be used to differentiate among ground-states with different entanglement properties. More specifically, we are able to differentiate between standard insulators and Z2 topologically ordered phases. We also find that certain non-local probes based on topological invariants can signal the insulating to superfluid phase transition.

Read in full at arXiv.

This is an abstract of a preprint hosted on an independent third party site. It has not been peer reviewed but is currently under consideration at Nature Communications.

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Nature Communications

Nature Research, Springer Nature