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Deviations from random-matrix entanglement statistics for kicked quantum chaotic spin-1/2 chains.

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Quantum chaotic systems typically follow random matrix theory. However, kicked spin-1/2 chains show deviations in eigenstate entanglement distribution, suggesting limitations of standard random matrix ensembles for these many-body systems.

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Area of Science:

  • Quantum mechanics
  • Many-body systems
  • Quantum chaos

Background:

  • Statistical properties of quantum chaotic many-body systems are expected to approach random matrix theory with increasing system size.
  • Eigenstate entanglement is a key statistical property in these systems.

Purpose of the Study:

  • To investigate the behavior of eigenstate entanglement in kicked spin-1/2 chain models.
  • To determine if these systems adhere to predictions from random matrix theory.

Main Methods:

  • Analysis of various kicked spin-1/2 chain models.
  • Comparison of eigenstate entanglement distributions with random matrix results.
  • Investigation of a tensor-product random matrix model with all-to-all interactions.

Main Results:

  • The average eigenstate entanglement in kicked spin-1/2 chains approaches random matrix results as system size increases.
  • The distribution of eigenstate entanglement shows significant deviations from random matrix predictions, even in scrambling systems.
  • Similar deviations were observed in a tensor-product random matrix model.

Conclusions:

  • The deviations in eigenstate entanglement are attributed to the tensor-product structure of the Hilbert spaces in these many-body systems.
  • Standard random matrix ensembles may not adequately describe the statistical properties of kicked spin-1/2 chain models.
  • This finding has implications for understanding quantum chaos in complex quantum systems.