Spreading of a local excitation in a quantum hierarchical model

We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. We provide analytical predictions for its time evolution, solving the single-particle dynamics on a hierarchical network. A localization mechanism is found, and the excitation remains close to its initial position at arbitrary times. Furthermore, a universal scaling among space and time is found that is related to the algebraic decay of the interactions as r-1-σ. We compare our predictions to numerics, employing tensor network techniques, for large magnetic fields, discussing the robustness of the mechanism in the full many-body dynamics.