Abstract
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 . 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.
- Received 3 August 2022
- Revised 9 October 2022
- Accepted 11 October 2022
DOI:https://doi.org/10.1103/PhysRevB.106.134210
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