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arXiv · 2006.15152

An exponential ramp in the quadratic Sachdev-Ye-Kitaev model

Michael Winer·Shao-Kai Jian·Brian Swingle
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Abstract

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.

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Michael Winer, Shao-Kai Jian, Brian Swingle. 2020-06-26. An exponential ramp in the quadratic Sachdev-Ye-Kitaev model. https://doi.org/10.1103/physrevlett.125.250602

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