• multipartite entanglement
• quantum fisher information
• quantum spin systems

The characterization of many-body quantum systems through their entanglement properties is an intruiguing problem at the verge of quantum information and many-body physics. The study of quantum systems from the perspective of information science allows a deeper understanding of many phenomena in which these systems are involved and allows to explore the possible applications for quantum technologies. Current studies have mainly focused on bipartite or pairwise entanglement in the ground state of critical Hamiltonians: these studies have emphasized a growth of entanglement in the vicinity of quantum critical points. However many-body quantum states show a richer structure of multiparticle correlations. Despite this, much less attention has been devoted to witnessing multipartite entanglement in quantum many-body systems. Yet, multipartite entanglement has been detected experimentally in atomic ensembles and a vivid line of research is currently focused on the study of possible witnesses that allows to detect multipartiticity in quantum states. Among these witnesses, the quantum Fisher information (QFI) has proved to be especially powerful: it extends the class of entangled states detectable by popular methods such as the spin squeezing, it can be extracted from experimental data and it has a physical interpretation in terms of distinguishability of quantum states after an external parametric transformations. In this thesis we investigate the behaviour of multipartite entanglement as detected by the quantum Fisher information of a spin-1/2 XXZ Heisenberg chain. The analysis is performed both at zero and finite temperature and in the presence of quenched disorder.