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

TL;DR

This paper investigates the spectral form factor in the two-body Sachdev-Ye-Kitaev model, revealing an exponential ramp due to high-dimensional saddle points, contrasting with the linear ramp in chaotic models, and discusses symmetry breaking effects.

Contribution

It uncovers a novel exponential ramp mechanism in the spectral form factor of a disordered integrable model, linked to a high-dimensional saddle point manifold and symmetry considerations.

Findings

Spectral form factor exhibits an exponential ramp in the two-body SYK model.

High-dimensional saddle points explain the exponential ramp.

Symmetry breaking transitions the ramp from exponential to linear.

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.