Bell Correlations at Ising Quantum Critical Points

When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a nonlocal behavior. Focusing on the Ising model in a transverse field with power-law (1/rα) ferromagnetic interaction...

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Bibliographic Details
Published in:Physical review letters 2019-10, Vol.123 (17), p.1-170604, Article 170604
Main Authors: Piga, Angelo, Aloy, Albert, Lewenstein, Maciej, Frérot, Irénée
Format: Article
Language:English
Subjects:
Bell's inequality
Correlation analysis
Critical point
Entangled states
Ferromagnetism
Invariants
Ising model
Variations
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Summary:When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a nonlocal behavior. Focusing on the Ising model in a transverse field with power-law (1/rα) ferromagnetic interactions, we show that a permutationally invariant Bell inequality based on two-body correlations is violated in the vicinity of the quantum-critical point. This observation, obtained via analytical spin-wave calculations and numerical density-matrix renormalization group computations, is traced back to the squeezing of collective-spin fluctuations generated by quantum-critical correlations. We observe a maximal violation for infinite-range interactions (α=0), namely, when interactions and correlations are themselves permutationally invariant.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.123.170604