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?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.

Entanglement entropy of the long-range Dyson hierarchical model / Pappalardi, S.; Calabrese, P.; Parisi, G.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2019:7(2019), pp. 1-29. [10.1088/1742-5468/ab2903]

Entanglement entropy of the long-range Dyson hierarchical model

Pappalardi, S.;Calabrese, P.;Parisi, G.
2019-01-01

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?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.
2019
2019
7
1
29
073102
https://arxiv.org/abs/1904.00015
Pappalardi, S.; Calabrese, P.; Parisi, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/108408
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