Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems
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Serbyn-2013-Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems.pdf
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Author(s)
Serbyn, Maksym
Abanin, Dmitry A.
Papic, Z.
Date Issued
June 2013
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Serbyn, Maksym, Z. Papić, and Dmitry A. Abanin. “Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems.” Physical Review Letters 110, no. 26 (June 2013). © 2013 American Physical Society
Version
Final published version
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/ℏ), 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.110.260601
