Many-body level statistics of single-particle quantum chaos

Understand

We consider a non-interacting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model) - a generic model of single-particle quantum chaos.

• We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation.
• Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape.
• In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction.