Abstract: In 1953 Feynman introduced permutation cycles of worldlines (particles
paths) inherent to the path integral description of quantum mechanics, to
study the superfluidity of liquid Helium and continuous systems.

In this talk I will present how permutation cycles can be exploited to
study Bose-Hubbard-type models, and the phases stabilized there in. We
will also see how they can be seen as simple topological invariant of
worldlines configurations, and exploited to extract some information on
the ground-state multipartite entanglement of such phases.