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.

Ref: Yin and Lucas, “Prethermalization and the local robustness of gapped systems”, Physical Review Letters 131 (5), 050402