Single-Particle Universality of the Many-Body Spectral Form Factor

• URL: http://arxiv.org/abs/2410.07306v2
• Date: Tue, 31 Dec 2024 19:02:24 GMT
• Title: Single-Particle Universality of the Many-Body Spectral Form Factor
• Authors: Michael O. Flynn, Lev Vidmar, Tatsuhiko N. Ikeda,
• Abstract summary: 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.
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• 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.

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