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

TitleAn exponential ramp in the quadratic Sachdev-Ye-Kitaev model
Publication TypeJournal Article
Year of Publication2020
AuthorsWiner, M, Jian, S-K, Swingle, B
Date Published6/26/2020

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.