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Spectral statistics in quantum many-body systems were analyzed. The study found that spatial dimension significantly impacts the many-body Thouless time, influencing deviations from random matrix theory predictions.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Chaotic quantum many-body systems exhibit complex spectral statistics.
  • Random matrix theory (RMT) often describes these statistics.
  • Lattice Floquet models provide a framework to study non-equilibrium quantum dynamics.

Purpose of the Study:

  • Investigate spectral statistics in spatially extended chaotic quantum many-body systems.
  • Analyze the behavior of the spectral form factor (K(t)).
  • Determine the influence of spatial dimensions and system size on spectral correlations.

Main Methods:

  • Utilized simple lattice Floquet models lacking time-reversal symmetry.
  • Employed analytical and numerical computations of the spectral form factor K(t).
  • Examined the many-body Thouless time (t_Th) and its dependence on system parameters.

Main Results:

  • The spectral form factor K(t) aligns with RMT for times exceeding the many-body Thouless time (t_Th).
  • t_Th shows a distinct dependence on spatial dimension (d) and system size.
  • In dimensions d>1, t_Th is finite and determined by intersite coupling.
  • In one dimension, t_Th diverges with system size, creating a window where spectral correlations deviate from RMT.

Conclusions:

  • The spatial dimension critically governs the emergence of RMT-like spectral statistics.
  • A many-body localization transition was observed in the Floquet model.
  • The spectral form factor's behavior in the localized phase was discussed.