Universal slow growth of entanglement in interacting strongly disordered systems

Maksym Serbyn, Z. Papić, Dmitry A. Abanin

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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.

Original languageEnglish (US)
Article number260601
JournalPhysical review letters
Volume110
Issue number26
DOIs
StatePublished - Jun 28 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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