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Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model.

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Researchers studied the spectral form factor in disordered integrable many-body models. They discovered an exponential ramp in the Sachdev-Ye-Kitaev model, differing from chaotic systems.

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Area of Science:

  • Quantum chaos
  • Many-body physics
  • Statistical mechanics

Background:

  • The spectral form factor (SFF) is a key diagnostic for quantum chaos, typically showing linear growth.
  • The behavior of SFF in disordered integrable many-body systems remains poorly understood.

Purpose of the Study:

  • Investigate the SFF in disordered integrable many-body models.
  • Contrast the SFF behavior with that of chaotic systems.
  • Elucidate the underlying mechanisms driving the observed SFF dynamics.

Main Methods:

  • Analysis of the two-body Sachdev-Ye-Kitaev (SYK) model.
  • Path integral formulation of the spectral form factor.
  • Investigation of saddle point structures in the path integral.

Main Results:

  • The SYK model exhibits an exponential ramp in its spectral form factor.
  • This exponential ramp contrasts sharply with the linear ramp observed in chaotic models.
  • A novel mechanism involving a high-dimensional manifold of saddle points, arising from large symmetry groups, explains the exponential ramp.

Conclusions:

  • Disordered integrable many-body models, exemplified by the SYK model, display distinct spectral dynamics compared to chaotic systems.
  • The presence of large symmetry groups leads to a manifold of saddle points, generating an exponential ramp in the SFF.
  • Finite nonintegrable interactions break down these symmetries, transitioning the SFF behavior towards a linear ramp.