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 H₀ be a Hamiltonian, spatially local in d spatial dimensions, with a gap Δ 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 ε << Δ. 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 time scale τ ~ exp[(Δ/ε)^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 H₀ was frustration-free. We infer the robustness of quantum simulation in low-energy subspaces, the existence of ``scarring" (strongly athermal correlation functions) in gapped systems subject to generic perturbations, 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.