Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions

Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, $S_{vN}(t)\propto t^γ$. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent $γ$ acquires a universal value $γ_c\simeq 0.33$ at the many-body localization transition, for different lattice models and decay powers. Moreover, our results suggest an intriguing relation between $γ_c$ and the critical minimal decay power of interactions necessary for the observation of many-body localization.

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