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An exponential ramp in the quadratic Sachdev-Ye-Kitaev model
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A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.
Forward citations
Cited by 2 Pith papers
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SYK spectral form factor moments match random matrix statistics at low order, with a k^2/N^{q-2} correction from spectral edge fluctuations that is amplified by sparsification.
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