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Quantum Ergodicity in the Many-Body Localization Problem.

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We generalized entanglement entropy calculations for random states to disordered many-body systems. Our findings challenge the idea of nonergodic extended states, revealing intrinsic correlations and thermal distributions in eigenstates.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Page's result provides a baseline for entanglement entropy in random pure states.
  • Understanding entanglement in realistic many-body systems is crucial for quantum information and condensed matter theory.

Purpose of the Study:

  • Generalize Page's result to disordered many-body systems with long-range interactions.
  • Investigate the nature of eigenstates and their distribution in energy shells.
  • Challenge existing concepts like nonergodic extended states.

Main Methods:

  • Generalization of Page's entanglement entropy formula.
  • Analysis of many-body eigenstates in disordered systems.
  • Comparison with exact diagonalization of the Sachdev-Ye-Kitaev (SYK) model.

Main Results:

  • Eigenstates in disordered systems occupy only a fraction of Fock space, exhibiting correlations absent in simpler models.
  • Preceding the many-body localization transition, eigenstates are thermally distributed across energy shells.
  • Results contradict the notion of nonergodic extended states.

Conclusions:

  • The structure of eigenstates in realistic disordered systems differs significantly from synthetic random models.
  • Thermal distribution of eigenstates is a key feature before many-body localization.
  • The concept of nonergodic extended states may require revision.