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

TL;DR

This paper uses out-of-time-ordered correlations to distinguish many-body localized phases from ergodic ones, identifying a logarithmic time variation and an order parameter for the transition.

Contribution

It introduces a novel application of OTO correlations to characterize MBL, including a localization length and a transition order parameter.

Findings

Logarithmic long-time variation of OTO correlation in MBL phase

Localization length depends logarithmically on interaction and diverges at critical point

OTOC fluctuation acts as an order parameter for ergodic-MBL transition

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.