Persistence of correlations in many-body localized spin chains

We study the evolution and persistence of quantum and classical correlations between spatially separated sites in the disordered XXZ spin chain in its ergodic and many-body-localized phases using exact diagonalization and matrix product state simulations. We show that in the many-body-localized phase, quantum entanglement survives in long-time unitary dynamics of the system, even though it is more fragile than the classical correlations. We study the dependence of the residual entanglement and correlations on the system size and on the disorder strength. Finally, we demonstrate the robustness of entanglement and correlations with respect to local dissipation in the bulk of the system.