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Characterizing many-body localization by out-of-time-ordered correlation

Rong-Qiang He and Zhong-Yi Lu
Phys. Rev. B 95, 054201 – Published 10 February 2017

Abstract

The out-of-time-ordered (OTO) correlation is a key quantity for quantifying quantum chaoticity and has been recently used in the investigation of quantum holography. Here we use it to study and characterize many-body localization (MBL). We find that a long-time logarithmic variation of the OTO correlation occurs in the MBL phase but is absent in the Anderson localized and ergodic phases. We extract a localization length in the MBL phase, which depends logarithmically on interaction and diverges at a critical interaction. Furthermore, the infinite-time “thermal” fluctuation of the OTO correlation is zero (finite) in the ergodic (MBL) phase and thus can be considered as an order parameter for the ergodic-MBL transition, through which the transition can be identified and characterized. Specifically, the critical point and the related critical exponents can be calculated.

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  • Received 20 August 2016

DOI:https://doi.org/10.1103/PhysRevB.95.054201

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Rong-Qiang He1,2,* and Zhong-Yi Lu2,†

  • 1Institute for Advanced Study, Tsinghua University, Beijing 100084, China
  • 2Department of Physics, Renmin University of China, Beijing 100872, China

  • *rqhe@ruc.edu.cn
  • zlu@ruc.edu.cn

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Issue

Vol. 95, Iss. 5 — 1 February 2017

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