**Abstract:** For a many-body local Hamiltonian H_0 perturbed by local V [H=H_0+V], one hopes in many scenarios that certain local properties of H_0 persist despite the fact that the extensive V strongly mixes the global eigenstates. For example, in the Hubbard model at large U, it is known that a doubly-occupied site needs an exponentially long time to decay into much less energetic single-particle excitations, a phenomenon called “prethermalization”. Such robustness is also demanded if one wants to store quantum information in the low-energy subspace of H_0, despite the presence of the unwanted V. In this talk, I will first survey known results on such problems with more examples, and then present a theorem that holds in the very general setting: We prove prethermalization for any gapped local many-body quantum system, subjected to small perturbations, in any spatial dimension. As applications, the theorem indicates the robustness of quantum simulation in low-energy subspaces, the existence of “scarring” (strongly athermal correlation functions) in perturbed gapped systems, the stability of false vacua in symmetry broken systems to non-perturbatively long times, and the robustness of quantum information in non-frustration-free gapped phases with topological order.

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Lunch will be provided at 12:00pm, so please come early to eat mingle and eat lunch before the talk begins.