Quantum information spreading in random spin chains

We study the spreading of quantum correlations and information in a one-dimensional quantum spin chain with critical disorder as encoded in an infinite randomness fixed point. Specifically, we focus on the dynamics after a quantum quench of the R\'enyi entropies, of the mutual information and of the entanglement negativity in the prototypical XXZ spin chain with random bonds and anisotropy parameters. We provide analytic predictions in the scaling regime based on real-space renormalization group methods. We support these findings through numerical simulations in the non-interacting limit, where we can access the scaling regime.