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

Understand

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, $S_{vN}(t)\propto t^{\gamma}$.
• Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent $\gamma$ acquires a universal value $\gamma_c\simeq 0.33$ at the many-body localization transition, for different lattice models and decay powers.