Recent studies found that the diffusive transport of conserved quantities in nonintegrable many-body systems has an imprint on quantum entanglement: while the von Neumann entropy of a state grows linearly in time $t$ under a global quench, all $n\mathrm{th}$ Rényi entropies with $n>1$ grow with a diffusive scaling $\sqrt{t}$. To understand this phenomenon, we introduce an amplitude $A\left(t\right)$, which is the overlap of the time evolution operator $U\left(t\right)$ of the entire system with the tensor product of the two evolution operators of the subsystems of a spatial bipartition. As long as $\left|A\left(t\right)\right|\ge e^{-\sqrt{Dt}}$, which we argue holds true for generic diffusive nonintegrable systems, all $n\mathrm{th}$ Rényi entropies with $n>1$ (annealed averaged over initial product states) are bounded from above by $\sqrt{t}$. We prove the following inequality for the disorder average of the amplitude, $\overline{\left|A\right(t\left)\right|}\ge e^{-\sqrt{Dt}}$, in a local spin-$\frac{1}{2}$ random circuit with a $\text{U}\left(1\right)$ conservation law by mapping to the survival probability of a symmetric exclusion process. Furthermore, we numerically show that the typical decay behaves asymptotically, for long times, as $\left|A\left(t\right)\right|\sim e^{-\sqrt{Dt}}$ in the same random circuit as well as in a prototypical nonintegrable model with diffusive energy transport but no disorder.

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Rényi纠缠熵的扩散标度

最近的研究发现，不可整合的多体系统中守恒量的扩散传输对量子纠缠有影响：而状态的冯·诺依曼熵随时间线性增长 $Ť$ 在全球范围内 $ñ日$ Rényi熵与 $ñ>\mathrm{1个}$ 以扩散比例增长 $\sqrt{Ť}$。为了理解这种现象，我们引入一个幅度$\mathrm{一种}（Ť）$，这是时间演化算子的​​重叠 $ü（Ť）$整个系统具有空间划分子系统的两个演化算子的​​张量积。只要$\left|\mathrm{一种}（Ť）\right|\ge {Ë}^{-\sqrt{dŤ}}$，对于一般的扩散不可积系统，我们认为 $ñ日$ Rényi熵与 $ñ>\mathrm{1个}$ （在初始产品状态下进行平均的退火处理）从上方受限制 $\sqrt{Ť}$。我们证明了振幅无序平均值的以下不等式，$\overline{|\mathrm{一种}（Ť）|}\ge {Ë}^{-\sqrt{dŤ}}$，在本地旋转$\frac{\mathrm{1个}}{2}$ 随机电路 $\text{ü}（\mathrm{1个}）$通过映射到对称排除过程的生存概率来守恒定律。此外，我们通过数值显示了长期以来，典型的衰变表现为渐近的$\left|\mathrm{一种}（Ť）\right|〜{Ë}^{-\sqrt{dŤ}}$ 在相同的随机电路中，以及在具有扩散能量传输但无障碍的原型非可积模型中。