论文标题
污染系统的局部鲁棒性
Prethermalization and the local robustness of gapped systems
论文作者
论文摘要
我们证明，在任何空间维度下，细度是局部多体量子系统的通用特性，受到小扰动。更确切地说，让$ h_0 $为hamiltonian，在$ d $ d $空间尺寸中的空间本地，在多体频谱中具有差距$δ$；让$ v $是一个在空间上的汉密尔顿，由本地术语组成，每个术语都由$ε\llδ$界定。然后，在本地操作员的相关函数中，量子动力学仅限于$ h_0 $的低能子空间是准确的，对于任何$ a <1/（2dd-1）$，对于拉伸指数时间尺度$τ\ sim \ sim \ sim \ exp [（Δ/ε）^a] $。该结果不取决于扰动是否缩小差距。在$ H_0 $无挫折的模型中，它显着扩大了先前的严格结果。我们推断出低能子空间中量子模拟的鲁棒性，在受一般扰动的含量中存在Athermal``sAcherd scared carared sawared sarded'sawared sard carared sarpared'sawared sard s carared saward sard s sard s sard s sard s sard s sard s sard s sard s sard s sard s saward sard s sar的相关功能，对对称性真空的较长寿命，在非折叠式系统中的质量信息的稳健性与非折叠式相关阶段的稳健性。
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 $ε\ll Δ$. 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 time scale $τ\sim \exp[(Δ/ε)^a]$ 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.
