The interplay of disorder and interactions in quantum systems can lead to several intriguing phenomena, amongst which the many-body localization (MBL) has attracted a lot of interest lately. MBL states challenge several of our common understanding of statistical mechanics: they do not thermalize, have a low entanglement, and can exhibit long-range order in one dimension at finite energy. After an introduction to the physics of MBL states, I will present our recent results [1] obtained large-scale numerics on the properties of eigenstates of the Heisenberg spin chain in a random field. Our energy-resolved computations allow to find evidence for the existence of a many-body mobility edge in such as system, separating ergodic and MBL phases. par noindent [1] David J. Luitz, Nicolas Laflorencie, Fabien Alet, arXiv:1411.0660

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