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Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model
Michael Winer1, Shao-Kai Jian1, Brian Swingle1
1Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
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.
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.
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