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Lieb-Robinson bounds and the structure of correlations in quantum many body systems


We give a simple proof of the Lieb-Robinson bounds and the existence of finite group velocity in quantum spin systems. We describe the consequences for quantum many body systems, like the clustering of correlations and the existence of a Lieb Mattis Schultz theorem in higher dimensions. We show recent results about the LR bounds in systems with topological order and extensions to infinite dimensional cases.