Spreading of a local excitation in a Quantum Hierarchical Model

TL;DR

This paper investigates how a local excitation propagates in a quantum hierarchical model, revealing a localization mechanism and universal scaling laws, supported by analytical solutions and tensor network simulations.

Contribution

It provides the first analytical and numerical analysis of excitation dynamics and localization in the quantum Dyson hierarchical model.

Findings

The excitation remains localized near its initial position at all times.

A universal space-time scaling law is identified related to algebraic decay of interactions.

Numerical simulations confirm the robustness of localization in many-body dynamics.

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.