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Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians.

Patrycja Łydżba1,2, Marcos Rigol3, Lev Vidmar1,4

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We introduce a method to distinguish quantum chaotic from integrable models using eigenstate entanglement entropy. Our findings provide a formula for this entropy, applicable to quantum systems like the Sachdev-Ye-Kitaev model.

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Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Eigenstate entanglement entropy is crucial for differentiating quantum chaotic and integrable models.
  • Integrable models exhibit volume-law entanglement with subsystem-dependent coefficients.
  • Quantum chaotic models show maximal, subsystem-independent entanglement entropy.

Purpose of the Study:

  • To derive a general analytical expression for average eigenstate entanglement entropy.
  • To establish a method for distinguishing quantum chaotic from integrable systems.
  • To validate the derived expression against numerical simulations and theoretical models.

Main Methods:

  • Utilizing random matrix theory for quadratic Hamiltonians.
  • Deriving a closed-form expression for entanglement entropy as a function of subsystem fraction.
  • Comparing analytical predictions with numerical data from the Sachdev-Ye-Kitaev model and the power-law random banded matrix model.

Main Results:

  • A closed-form expression for average eigenstate entanglement entropy was obtained.
  • The derived expression accurately describes numerical results for quantum chaotic models.
  • Deviations were observed due to localization effects in quasimomentum space.

Conclusions:

  • The derived formula provides a robust tool for classifying quantum models based on entanglement.
  • The study highlights the impact of localization on entanglement entropy predictions.
  • This work advances the understanding of quantum chaos and integrability through entanglement measures.