Spreading of a local excitation in a Quantum Hierarchical Model
- URL: http://arxiv.org/abs/2207.06790v2
- Date: Thu, 10 Nov 2022 13:21:53 GMT
- Title: Spreading of a local excitation in a Quantum Hierarchical Model
- Authors: Luca Capizzi, Guido Giachetti, Alessandro Santini and Mario Collura
- Abstract summary: 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.
A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
- Score: 62.997667081978825
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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