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Quantum many-body systems exhibiting random matrix theory (RMT) statistics may still show deviations in entanglement entropy. This study reveals that specific k-spin interactions, not RMT, drive these deviations in quantum chaotic systems.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Quantum many-body systems are often classified as quantum chaotic based on spectral statistics aligning with random matrix theory (RMT).
  • RMT predictions typically extend to other properties, including entanglement entropy, which is expected to follow a Page curve.

Purpose of the Study:

  • To investigate deviations from RMT predictions in entanglement entropy within a quantum chaotic system.
  • To identify the underlying mechanisms responsible for these deviations.

Main Methods:

  • Analysis of the kicked Ising chain, a model quantum many-body system.
  • Comparison of spectral and eigenvector statistics with RMT predictions.
  • Examination of entanglement entropy and its deviation from the Page curve.
  • Development and analysis of a quantity based on the effective Hamiltonian, focusing on the distribution of effective spin interaction strengths.

Main Results:

  • The kicked Ising chain exhibits spectral and eigenvector statistics consistent with RMT.
  • Despite RMT agreement, entanglement entropy deviates from the predicted Page curve.
  • Deviations are attributed to the behavior of k-spin interactions, particularly for k > 2.
  • Analysis of effective spin interaction strengths reveals significant differences compared to RMT predictions.

Conclusions:

  • Spectral and eigenvector statistics agreeing with RMT do not guarantee RMT-compliant entanglement entropy in quantum many-body systems.
  • The behavior of multi-spin interactions (k-spin) is crucial for understanding entanglement entropy deviations.
  • The proposed analysis of effective Hamiltonians provides a method to explain these deviations in quantum chaotic systems.