Out-of-time-order correlation for many-body localization

作     者：Ruihua Fan Pengfei Zhang Huitao Shen Hui Zhai 

作者机构：lnstitute for Advanced Study Tsinghua University Beijing 100084 China Department of Physics Peking University Beijing 100871 China Department of Physics Massachusetts Institute of Technology Cambridge MA 02139 USA Collaborative Innovation Center of Quantum Matter Beijing 100084 China 

出 版 物：《Science Bulletin》 (科学通报（英文版）)

年 卷 期：2017年第62卷第10期

页      面：707-711页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：supported by the National Key Research and Development Plan (2016YFA0301600) the National Natural Science Foundation of China (11325418) Tsinghua University Initiative Scientific Research Program 

主　　题：Out of time order correlationMany body localizationR6nyi entropy 

摘      要：In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.