Randomness and Chaos in Qubit Models

Understand

We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos.

• Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$ SYK$_2$ model at high temperatures that is absent in the $N=2$ SYK$_2$ model.
• Our results suggest that this dip-ramp-plateau behavior implies the existence of random eigenvectors in a quantum many-body system.
• To further support this observation, we examine the Gaussian random transverse Ising model and obtain consistent results without suffering from small $N$ issues.