Entanglement entropy of the long-range Dyson hierarchical model

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 $r^{-1-\sigma }$. 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 $\sigma$ that are tested against the numerical solution of the recursive equations.

27 pages, 11 figures

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• Negativity Spectrum in the Random Singlet Phase
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Entanglement entropy of the long-range Dyson hierarchical model
• Quantum information spreading in random spin chains
• Mutual information for fermionic systems
• Spreading of a local excitation in a Quantum Hierarchical Model
• Measurement-induced criticality in extended and long-range unitary circuits