Ground states of antiferromagnetic hierarchical Dyson models

Fumihiko Takano, Taeko Ogawa

文彦 高野, 多恵子 小川

Carlos Henrique Costa Moreira, Ricardo S. Schor

Silvia Pappalardi, Pasquale Calabrese, Giorgio Parisi A

Abstract We study the ground state entanglement entropy of the quantum Dyson hierarchical spin chain in which the interaction decays algebraically with the distance as . We exploit the real-space renormalisation group solution which gives the ground-state wave function in the form of a tree tensor network and provides a manageable recursive expression for the reduced density matrix of the renormalised ground state. Surprisingly, we find that at criticality the entanglement entropy obeys an area law, as opposite to the logarithmic scaling of short-range critical systems and of other non-hierarchical long-range models. We provide also some analytical results in the limit of large and small that are tested against the numerical solution of the recursive equations.

Azer Kerimov

Luca Capizzi, Guido Giachetti, Alessandro Santini +1 more

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 ${r}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\sigma}}$. 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.