Entanglement negativity in free lattice models

In pure states of many-body quantum systems, entanglement is routinely studied via the Renyi entropies, which give a complete characterization of the bipartite case. The situation becomes more complicated for mixed states, e.g. if the system is composed of more than two parts, and one is interested in the entanglement between two non-complementary pieces. In such a scenario the entanglement can be characterized by a suitable measure called logarithmic negativity which has been the focus of recent interest. Similarly to pure-state entanglement, most of our analytical understanding of negativity in many-body lattice systems originates from studying Gaussian states. In this talk I would like to give an overview about the available methods to extract information about the entanglement negativity in free lattice models. In particular, I will present some new results on tripartite entanglement in ground states of critical lattice models in one and two dimensions and, furthermore, even for systems driven far from equilibrium.