Single-Particle Universality of the Many-Body Spectral Form Factor
arXiv:2410.07306 · doi:10.1103/PhysRevLett.134.160403
Abstract
We consider systems of fermions evolved by non-interacting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the single-particle sector exhibits chaotic dynamics. We study the corresponding many-body spectral statistics and show that the spectral form factor (SFF) can be computed \textit{exactly}. Due to the absence of interactions the SFF grows exponentially in time, a result which we demonstrate through simple arguments, scaling collapses, and closed-form evaluation of the SFF. We study the role of interactions by numerically analyzing a kicked Ising model and find that the SFF crosses over to a linear growth regime consistent with many-body random matrix universality. Our exact results for the SFF provide a baseline for future studies of the crossover between single-particle and many-body random matrix behavior.
arXiv commentA companion paper titled "Exact spectral form factors of non-interacting fermions with Dyson statistics" is available at arXiv:2410.07306 and contains proofs of technical claims made here. Comments welcome!
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