标题： 纠缠扩散与布朗 SYK 链中的涌现局域性 显示英文标题

标题： Entanglement spreading and emergent locality in Brownian SYK chains

摘要： Ryu-Takayanagi（RT）公式及其在量子纠错码（QEC）方面的解释表明，在全息共形场论（CFT）中，量子信息的传播出现了一种涌现的局部性，其中在边界理论中某一点注入的信息在对应于蝴蝶速度的尖锐光锥内传播。 这种涌现的局部性是存在一个具有类似RT公式的纠缠熵的几何体对偶的必要条件。 在本文中，我们使用量子纠错码的工具来研究量子信息的传播以及在一种可解析处理的混沌动力学模型——一维布朗SYK链中尖锐光锥的出现。 我们从该模型中的无限温度态开始，并在时间$t=0$在链上的某一点$p$注入一个量子位。 然后我们显式计算在某个稍后的时间$t=T$，长度为$2\ell$的区间（围绕$p$）中包含的量子位的信息量。 我们发现，在强耦合下，这个量随着$\ell$的变化表现出从接近零到接近最大相关性的尖锐跃迁。 在$\ell \sim v_B T$处发生转变，$v_B$是蝴蝶速度。 这种尖锐光锥的出现源于一个称为 FKPP 方程的非线性扩散方程的推广，该方程在晚期时间和强耦合下接受尖锐的域墙解。 从混沌系统中算符增长的性质可以物理地理解这些域墙解。 显示英文摘要

摘要： The Ryu-Takayanagi (RT) formula and its interpretation in terms of quantum error correction (QEC) implies an emergent locality for the spread of quantum information in holographic CFTs, where information injected at a point in the boundary theory spreads within a sharp light-cone corresponding to the butterfly velocity. This emergent locality is a necessary condition for the existence of a geometric bulk dual with an RT-like formula for entanglement entropy. In this paper, we use tools from QEC to study the spread of quantum information and the emergence of a sharp light-cone in an analytically tractable model of chaotic dynamics, namely a one-dimensional Brownian SYK chain. We start with an infinite temperature state in this model and inject a qudit at time $t=0$ at some point $p$ on the chain. We then explicitly calculate the amount of information of the qudit contained in an interval of length $2\ell$ (centered around $p$) at some later time $t=T$. We find that at strong coupling, this quantity shows a sharp transition as a function of $\ell$ from near zero to near maximal correlation. The transition occurs at $\ell \sim v_B T$, with $v_B$ being the butterfly velocity. Underlying the emergence of this sharp light-cone is a non-linear generalization of the diffusion equation called the FKPP equation, which admits sharp domain wall solutions at late times and strong coupling. These domain wall solutions can be understood on physical grounds from properties of operator growth in chaotic systems.