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Recent results and open problems on many-body localization

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Periodic and Ergodic Spectral Problems

In the most recent decade the topic of many-body localization, understood as the absence of thermalization in interacting quantum many-body systems, has seen strong attention and rapid development in the physics literature. We will survey the relatively small number of mathematically rigorous results on MBL which have been obtained, in particular for disordered oscillator systems and some models of quantum spin chains. Specifically, we will consider manifestations of MBL such as absence of many-body transport, exponential decay of ground and thermal state correlations, as well as area laws for the entanglement of states. We will also mention some of the many open problems in this field.

This talk is part of the Isaac Newton Institute Seminar Series series.

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