Entanglement is a fundamental property of quantum mechanics, and plays an increasing role in our understanding of many-body systems, in and out of equilibrium. In multipartite systems, different forms of entanglement can exist between various sets of particles, and its detection, even theoretical, remains an outstanding challenge. In this talk, I will discuss criteria for such collective non-local quantum correlations in physical systems under very general conditions. For instance, at what temperatures can multipartite entanglement of a given kind exist? I will begin by explaining important properties about the space of physical states, and how these determine the fate of entanglement under the evolution of a system with temperature, time or separation. I will then illustrate these results with a simple yet generic model: the anti-ferromagnetic Ising model on an icosahedral molecule. Finally, I will discuss the fate of entanglement for Fermionic systems, where the parity superselection rule greatly modifies the geometry of the space of states and the structure of entanglement.

Based on work with W. Witczak-Krempa.