Entanglement growth in many-body localized systems with long-range interactions

We study the time evolution of one-dimensional systems of fermions with long-range interactions in the presence of strong disorder. Exact diagonalization of small systems supports many-body localization for weak Coulomb and dipolar interactions at high energy. The dephasing time of far apart degrees of freedom is analyzed. The result indicates that von Neumann entropy of one halve of the system evolves as a power law on time for a disentangled initial state. The numerical simulations performed in the Coulomb and dipolar cases are consistent with this prediction.