Spectral Form Factor in Sparse SYK Models

TL;DR

This paper studies the spectral form factor in sparse SYK models, showing that at intermediate times, fluctuations dominate the spectral correlations, which was previously conjectured but not numerically confirmed due to computational limitations.

Contribution

It provides numerical evidence that fluctuations, not new saddle points, dominate the spectral form factor in sparse SYK models at intermediate times.

Findings

Connected spectral form factor dominates at intermediate times

Fluctuations around disconnected geometry are responsible for this dominance

Previous conjectures about similar effects are supported by numerical results

Abstract

We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value of $N$ out of reach of current numerical simulations.