标题： 时间有序关联函数和随机场 XX 自旋链中的纠缠增长 显示英文标题

标题： Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain

摘要： 我们研究了在开放边界条件下，使用精确的Jordan-Wigner变换到费米子哈密顿量的随机场XX模型中的时间序相关性，$C(x,t)$和纠缠增长。对于任何非零强度的随机场，该模型描述了一个安德森绝缘体。考虑了两种情景：初始状态对应于Néel形式的乘积态的全局淬火，以及在典型热态下的行为，$\beta=1$。由于存在无序，由时间序相关性描述的信息传播在典型的长度尺度之外停止，$\xi_{OTOC}$。对于$|x|<\xi_{OTOC}$，信息传播以最大速度$v_{max}=J$发生，并且我们确认了$C(x,t)\sim t^{2|x|}$早期时间行为的预测。对于从Néel乘积态开始的淬火情况，我们还研究了双部分纠缠的增长，重点放在晚期和无限时间的行为上。观察到对于我们研究的无序强度，接近有限纠缠的过程是缓慢的。 显示英文摘要

摘要： We study out of time order correlations, $C(x,t)$ and entanglement growth in the random field XX model with open boundary conditions using the exact Jordan-Wigner transformation to a fermionic Hamiltonian. For any non-zero strength of the random field this model describes an Anderson insulator. Two scenarios are considered: A global quench with the initial state corresponding to a product state of the N\'eel form, and the behaviour in a typical thermal state at $\beta=1$. As a result of the presence of disorder the information spreading as described by the out of time correlations stops beyond a typical length scale, $\xi_{OTOC}$. For $|x|<\xi_{OTOC}$ information spreading occurs at the maximal velocity $v_{max}=J$ and we confirm predictions for the early time behaviour of $C(x,t)\sim t^{2|x|}$. For the case of the quench starting from the N\'eel product state we also study the growth of the bipartite entanglement, focusing on the late and infinite time behaviour. The approach to a bounded entanglement is observed to be slow for the disorder strengths we study.