Bounded Entanglement Entropy in the Quantum Ising Model

A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grim...

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Bibliographic Details
Published inJournal of statistical physics Vol. 178; no. 1; pp. 281 - 296
Main Authors Grimmett, Geoffrey R., Osborne, Tobias J., Scudo, Petra F.
Format Journal Article
LanguageEnglish
Published New York Springer US 2020
Springer
Springer Nature B.V
Subjects
Entropy
Ising model
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum entanglement
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Quantum Ising model
Entanglement
Entropy
82B20
Area law
60K35
Random-cluster model
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Summary:A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grimmett et al. (J Stat Phys 131:305–339, 2008). The proof utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-019-02432-y