标题： 多体局域系统动力学：对数光锥和$\log \, t$-定律的$α$-Rényi 熵 显示英文标题

标题： Dynamics of many-body localized systems: logarithmic lightcones and $\log \, t$-law of $α$-Rényi entropies

摘要： 在多体局域化现象学的背景下，我们考虑任意大的一维自旋系统。 具有无序的XXZ模型是一个典型的例子。 在不假设存在指数局域化的守恒量（LIOMs）的情况下，而是假设对数光锥，我们严格评估了$ \alpha$-Rényi熵的动力学生成，$ 0< \alpha<1 $接近于一，得到一个$\log \, t$-定律。 假设LIOMs的存在，我们证明了系统动力学的Lieb-Robinson（L-R）界具有对数光锥，并表明从一般的初始乘积态出发，冯·诺依曼熵的动力学生成在长时间下具有$ \log \, t$-形状。 量化局部算子动力学扩展的L-R界，在与纠缠等全局量相比时，可能更容易在实验中测量。 显示英文摘要

摘要： In the context of the Many-Body-Localization phenomenology we consider arbitrarily large one-dimensional spin systems. The XXZ model with disorder is a prototypical example. Without assuming the existence of exponentially localized integrals of motion (LIOMs), but assuming instead a logarithmic lightcone we rigorously evaluate the dynamical generation of $ \alpha$-R\'enyi entropies, $ 0< \alpha<1 $ close to one, obtaining a $\log \, t$-law. Assuming the existence of LIOMs we prove that the Lieb-Robinson (L-R) bound of the system's dynamics has a logarithmic lightcone and show that the dynamical generation of the von Neumann entropy, from a generic initial product state, has for large times a $ \log \, t$-shape. L-R bounds, that quantify the dynamical spreading of local operators, may be easier to measure in experiments in comparison to global quantities such as entanglement.