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Slow Growth of Out-of-Time-Order Correlators and Entanglement Entropy in Integrable Disordered Systems.

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

McGinley, Maximilian  ORCID logo  https://orcid.org/0000-0003-3122-2207
Nunnenkamp, Andreas  ORCID logo  https://orcid.org/0000-0003-2390-7636
Knolle, Johannes 

Abstract

We investigate how information spreads in three paradigmatic one-dimensional models with spatial disorder. The models we consider are unitarily related to a system of free fermions and, thus, are manifestly integrable. We demonstrate that out-of-time-order correlators can spread slowly beyond the single-particle localization length, despite the absence of many-body interactions. This phenomenon is shown to be due to the nonlocal relationship between elementary excitations and the physical degrees of freedom. We argue that this nonlocality becomes relevant for time-dependent correlation functions. In addition, a slow logarithmic-in-time growth of the entanglement entropy is observed following a quench from an unentangled initial state. We attribute this growth to the presence of strong zero modes, which gives rise to an exponential hierarchy of time scales upon ensemble averaging. Our work on disordered integrable systems complements the rich phenomenology of information spreading and we discuss broader implications for general systems with nonlocal correlations.

Description

Keywords

cond-mat.str-el, cond-mat.str-el, cond-mat.dis-nn, cond-mat.mes-hall, cond-mat.stat-mech

Journal Title

Phys Rev Lett

Conference Name

Journal ISSN

0031-9007
1079-7114

Volume Title

122

Publisher

American Physical Society (APS)
Sponsorship
The Royal Society (uf130303)