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

Ruihua Fan; Pengfei Zhang; Huitao Shen; Hui Zhai

doi:10.1016/j.scib.2017.04.011

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

Sci Bull (Beijing). 2017 May 30;62(10):707-711. doi: 10.1016/j.scib.2017.04.011. Epub 2017 Apr 20.

Authors

Ruihua Fan¹, Pengfei Zhang², Huitao Shen³, Hui Zhai⁴

Affiliations

¹ Institute for Advanced Study, Tsinghua University, Beijing 100084, China; Department of Physics, Peking University, Beijing 100871, China.
² Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
³ Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
⁴ Institute for Advanced Study, Tsinghua University, Beijing 100084, China; Collaborative Innovation Center of Quantum Matter, Beijing 100084, China. Electronic address: hzhai@tsinghua.edu.cn.

PMID: 36659442
DOI: 10.1016/j.scib.2017.04.011

Abstract

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 Rényi 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.

Keywords: Many-body localization; Out-of-time-order correlation; Rényi entropy.