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Extended slow dynamical regime close to the many-body localization transition

David J. Luitz, Nicolas Laflorencie, and Fabien Alet
Phys. Rev. B 93, 060201(R) – Published 17 February 2016

Abstract

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L=28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S(t)t1/z with a disorder-dependent exponent z1, in contrast with the pure ballistic growth z=1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I(t)tζ with a continuously varying disorder-dependent exponent ζ, vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.

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  • Received 30 November 2015

DOI:https://doi.org/10.1103/PhysRevB.93.060201

©2016 American Physical Society

Authors & Affiliations

David J. Luitz1,2,*, Nicolas Laflorencie2,†, and Fabien Alet2,‡

  • 1Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 2Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, 31062 Toulouse, France

  • *dluitz@illinois.edu
  • laflo@irsamc.ups-tlse.fr
  • alet@irsamc.ups-tlse.fr

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Issue

Vol. 93, Iss. 6 — 1 February 2016

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