Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems

Maksym Serbyn, Z. Papić, and Dmitry A. Abanin
Phys. Rev. Lett. 110, 260601 – Published 28 June 2013

Abstract

Recent numerical work by Bardarson, Pollmann, and Moore revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states. For weak interactions, we find that the entanglement entropy grows as ξln(Vt/), where V is the interaction strength, and ξ is the single-particle localization length. The saturated value of the entanglement entropy at long times is determined by the participation ratios of the initial state over the eigenstates of the subsystem. Our work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase.

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  • Received 24 April 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.260601

© 2013 American Physical Society

Authors & Affiliations

Maksym Serbyn1, Z. Papić2, and Dmitry A. Abanin3,4

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02138, USA
  • 2Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 4Institute for Quantum Computing, Waterloo, Ontario N2L 3G1, Canada

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Issue

Vol. 110, Iss. 26 — 28 June 2013

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