  We provide insight in the quantum correlations structure present in strongly
correlated systems beyond the standard framework of bipartite entanglement. To
this aim we first exploit rotationally invariant states as a test bed to detect
genuine tripartite entanglement beyond the nearest-neighbor in spin-1/2 models.
Then we construct in a closed analytical form a family of entanglement
witnesses which provides a sufficient condition to determine if a state of a
many-body system formed by an arbitrary number of spin-1/2 particles possesses
genuine tripartite entanglement, independently of the details of the model. We
illustrate our method by analyzing in detail the anisotropic XXZ spin chain
close to its phase transitions, where we demonstrate the presence of long range
multipartite entanglement near the critical point and the breaking of the
symmetries associated to the quantum phase transition.
