Prethermalization and the local robustness of gapped systems

• URL: http://arxiv.org/abs/2209.11242v2
• Date: Tue, 18 Apr 2023 00:23:39 GMT
• Title: Prethermalization and the local robustness of gapped systems
• Authors: Chao Yin, Andrew Lucas
• Abstract summary: We prove that prethermalization is a generic property of gapped local many-body quantum systems. We infer the robustness of quantum simulation in low-energy subspaces.
• Score: 0.22843885788439797
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\Delta$ 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 $\epsilon \ll \Delta$. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of $H_0$ is accurate, in the correlation functions of local operators, for stretched exponential time scale $\tau \sim \exp[(\Delta/\epsilon)^a]$ 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.

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