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

Max McGinley, Andreas Nunnenkamp, and Johannes Knolle
Phys. Rev. Lett. 122, 020603 – Published 16 January 2019
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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.

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  • Received 16 July 2018
  • Revised 11 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.020603

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGeneral PhysicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Max McGinley1, Andreas Nunnenkamp1, and Johannes Knolle2,1

  • 1Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
  • 2Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom

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Issue

Vol. 122, Iss. 2 — 18 January 2019

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