article published Maksym Serbyn author 47809E7E-F248-11E8-B48F-1D18A9856A870000-0002-2399-5827 Zlatko Papić author Dmitry Abanin author 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. American Physical Society2013 10.1103/PhysRevLett.110.260601 11026 yes M. Serbyn, Z. Papić, and D. Abanin, “Universal slow growth of entanglement in interacting strongly disordered systems,” <i>Physical Review Letters</i>, vol. 110, no. 26. American Physical Society, 2013. M. Serbyn, Z. Papić, D. Abanin, Physical Review Letters 110 (2013). Serbyn M, Papić Z, Abanin D. 2013. Universal slow growth of entanglement in interacting strongly disordered systems. Physical Review Letters. 110(26). Serbyn M, Papić Z, Abanin D. Universal slow growth of entanglement in interacting strongly disordered systems. <i>Physical Review Letters</i>. 2013;110(26). doi:<a href="https://doi.org/10.1103/PhysRevLett.110.260601">10.1103/PhysRevLett.110.260601</a> Serbyn, M., Papić, Z., &#38; Abanin, D. (2013). Universal slow growth of entanglement in interacting strongly disordered systems. <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevLett.110.260601">https://doi.org/10.1103/PhysRevLett.110.260601</a> Serbyn, Maksym, Zlatko Papić, and Dmitry Abanin. “Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems.” <i>Physical Review Letters</i>. American Physical Society, 2013. <a href="https://doi.org/10.1103/PhysRevLett.110.260601">https://doi.org/10.1103/PhysRevLett.110.260601</a>. Serbyn, Maksym, et al. “Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems.” <i>Physical Review Letters</i>, vol. 110, no. 26, American Physical Society, 2013, doi:<a href="https://doi.org/10.1103/PhysRevLett.110.260601">10.1103/PhysRevLett.110.260601</a>. 9752018-12-11T11:49:29Z2021-01-12T08:22:22Z