Out-of-Time-Order Correlation for Many-Body Localization

TL;DR

This paper investigates out-of-time-order correlators (OTOC) in many-body localized systems, showing their power to distinguish phases and relating their decay to entropy growth, with broad theoretical implications.

Contribution

It provides the first detailed analysis of OTOC behavior in many-body localized phases and establishes a general theorem linking OTOC decay to entropy growth.

Findings

OTOC decreases as a power law at the scrambling time in MBL systems

OTOC can distinguish MBL from Anderson localization, unlike normal correlators

A theorem relates OTOC decay to second Rényi entropy growth in generic quantum systems

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 R\'enyi 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.