Prethermalization and the Local Robustness of Gapped Systems.
Phys Rev Lett
; 131(5): 050402, 2023 Aug 04.
Article
in En
| MEDLINE
| ID: mdl-37595215
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 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 εâªΔ. 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 timescale τâ¼exp[(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 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.
Full text:
1
Database:
MEDLINE
Language:
En
Journal:
Phys Rev Lett
Year:
2023
Type:
Article
Affiliation country:
United States