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Distant observers sharing entangled quantum states can exhibit nonlocal behavior. This study shows a many-body Bell inequality violation in the Ising model near its quantum-critical point due to spin fluctuations.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Entangled quantum states allow distant observers to exhibit correlations that defy classical explanations.
  • Many-body Bell inequalities are crucial for demonstrating quantum nonlocality in complex systems.
  • The Ising model in a transverse field is a fundamental model for studying quantum phase transitions.

Purpose of the Study:

  • To investigate the violation of a many-body Bell inequality in the Ising model with power-law interactions.
  • To identify the underlying quantum correlations responsible for nonlocality near a quantum-critical point.
  • To explore the role of collective-spin fluctuations in demonstrating quantum nonlocality.

Main Methods:

  • Analytical spin-wave calculations to probe quantum correlations.
  • Numerical density-matrix renormalization group (DMRG) computations for system analysis.
  • Investigation of a permutationally invariant Bell inequality based on two-body correlations.

Main Results:

  • A permutationally invariant Bell inequality is violated near the quantum-critical point of the Ising model.
  • The violation is attributed to the squeezing of collective-spin fluctuations driven by quantum-critical correlations.
  • Maximal violation occurs for infinite-range interactions (α=0), where correlations are permutationally invariant.

Conclusions:

  • Quantum-critical correlations in the Ising model can lead to observable nonlocality.
  • The study provides a mechanism for detecting quantum nonlocality in many-body systems.
  • The findings highlight the importance of collective spin dynamics in quantum information science.