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arXiv · 1608.03586

Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation

Rong-Qiang He·Zhong-Yi Lu
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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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BibTeXRIS

Rong-Qiang He, Zhong-Yi Lu. 2016-08-11. Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation. https://doi.org/10.1103/physrevb.95.054201

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