Abstract
We analyze a family of 1D fully analytically solvable models in which a many-body cluster interaction, acting simulatenously on n + 2 spins, competes with a uniform transverse external field. These models can be solved analytically using the Jordan–Wigner transformations and we prove that they present a very rich phase diagram with both nematic and symmetry protected topological ordered phases. From the point of view of the entanglement, these models show a non vanishing bipartite entanglement between the spins at the end points of the cluster term. At the same time, regardless to the system parameters, it is possible to prove analytically that there in no genuine multipartite entanglement among the spins of a subset made by . Numerical simulations suggest that this absence extends also to larger subsets. Due to their integrability and to the peculiar entanglement properties, the n-cluster models in a transverse magnetic field may serve as a prototype for studying non trivial order and can be of extreme relevance for applications of quantum information tasks.
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