Yin Chao, Lucas Andrew
Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev Lett. 2023 Aug 4;131(5):050402. doi: 10.1103/PhysRevLett.131.050402.
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 ε≪Δ. 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 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 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.
我们证明，在任何空间维度下，带隙的局域多体量子系统在受到小扰动时，预热化是一种普遍性质。更确切地说，设(H_{0})是一个哈密顿量，在(d)个空间维度上具有空间局域性，其多体谱中有一个能隙(\Delta)；设(V)是一个空间局域的哈密顿量，由局域项之和组成，每个局域项的量级为(\varepsilon\ll\Delta)。那么，对于任何(a < 1/(2d - 1))，在拉伸指数时间尺度(\tau\sim\exp[(\Delta / \varepsilon)^{a}])下，量子动力学限制在(H_{0})的低能子空间这一近似在局域算符的关联函数中是精确的。该结果不依赖于扰动是否会使能隙闭合。它显著扩展了之前关于(H_{0})无受挫模型中预热化的严格结果。我们推断出低能子空间中量子模拟的稳健性、受一般扰动的带隙系统中存在非热的“疤痕”关联函数、对称破缺系统中虚假真空的长寿命以及具有拓扑序的非无受挫带隙相中的量子信息的稳健性。
