Prethermalization and the Local Robustness of Gapped Systems

We prove that prethermalization is a generic property of gapped local many-body quantum systems, subjected to small perturbations, in any spatial dimension. More precisely, let H-0 be a Hamiltonian, spatially local in d spatial dimensions, with a gap A in the many-body spectrum; let V be a spatially local Hamiltonian consisting of a sum of local terms, each of which is bounded by epsilon << Delta. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of H0 is accurate, in the correlation functions of local operators, for stretched exponential timescale tau similar to exp[(Delta/epsilon)(a)] for any a < 1/(2d - 1). This result does not depend on whether the perturbation closes the gap. It significantly extends previous rigorous results on prethermalization in models where H-0 was frustration-free. We infer the robustness of quantum simulation in low-energy subspaces, the existence of athermal "scarred" correlation functions in gapped systems subject to generic perturbations, the long lifetime of false vacua in symmetry broken systems, and the robustness of quantum information in non-frustration-free gapped phases with topological order.