Information delocalization in many body systems: From MBL phases to black holes

This is a short review of several articles of the authors on the issue of information delocalization in many-body physics, to appear in the proceedings of ‘Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory’, held in Natal 2015. Motivated by problems in black hole physics, expander graphs, and MBL phases, we developed an approach to information delocalization based on Mutual Information (MI). Intuitively, given a subsystem A, we looks at the support of the minimal subsystem B which is maximally entangled with A. This support can be computed analytically for random states, setting the intuition for non-equilibrium scenarios. We describe its behavior in a wide range of models, such as chaotic spin chains, Many-Body-Localized (MBL) phases, and systems displaying large-N factorization. For the last class of models, and as expected from the AdS/CFT correspondence, we find similar results when studying entropy evolution in black hole collapse scenarios.