Many-body level statistics of single-particle quantum chaos

TL;DR

This paper analyzes the spectral statistics of many-fermion systems in a quantum chaos setting, revealing universal features like an exponential ramp in the spectral form factor despite integrability.

Contribution

It provides an analytical calculation of the many-body spectral form factor for a non-interacting fermion model related to quantum chaos, uncovering universal spectral features.

Findings

Residual level repulsion due to single-particle chaos

Presence of islands of level attraction

Universal exponential ramp in spectral form factor

Abstract

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. These results are encoded in an exponential ramp in the spectral form-factor, which we show to be a universal feature of non-ergodic many-fermion systems embedded in a chaotic medium.