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arXiv · 2207.06790

Spreading of a local excitation in a Quantum Hierarchical Model

Luca Capizzi·Guido Giachetti·Alessandro Santini·Mario Collura
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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 related to the algebraic decay of the interactions as $r^{-1-\sigma}$. 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.

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Luca Capizzi, Guido Giachetti, Alessandro Santini, Mario Collura. 2022-07-14. Spreading of a local excitation in a Quantum Hierarchical Model. https://doi.org/10.1103/physrevb.106.134210

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