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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Wigner-Dyson statistics describe energy level distributions in quantum systems.
  • The Gaussian β ensemble generalizes these statistics to a continuous range of β.
  • Many-body localization (MBL) describes a transition from thermal to localized behavior in interacting quantum systems.

Purpose of the Study:

  • To numerically investigate the level statistics of the Gaussian β ensemble.
  • To establish the physical relevance of these statistics in the context of many-body localization.
  • To explore the behavior of the Gaussian β ensemble for Hamiltonians with broken time-reversal symmetry.

Main Methods:

  • Numerical simulations of the Gaussian β ensemble.
  • Comparison of level statistics with a paradigmatic MBL model.
  • Analysis of a related Hamiltonian with broken time-reversal symmetry.

Main Results:

  • The Gaussian β ensemble provides a smooth interpolation between Poissonian (β→0) and Wigner-Dyson (β=1, 2, 4) level statistics.
  • Excellent agreement was found between the Gaussian β ensemble statistics and the MBL model across the thermal-to-localized phase transition.
  • Similar agreement was observed for a Hamiltonian with broken time-reversal symmetry.

Conclusions:

  • The Gaussian β ensemble is physically relevant for describing level statistics in complex quantum systems.
  • These statistics accurately capture the behavior of systems undergoing many-body localization.
  • The framework extends to systems with broken time-reversal symmetry, broadening its applicability.