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arXiv · 2410.07306

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

Michael O. Flynn·Lev Vidmar·Tatsuhiko N. Ikeda
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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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Michael O. Flynn, Lev Vidmar, Tatsuhiko N. Ikeda. 2024-10-09. Single-Particle Universality of the Many-Body Spectral Form Factor. https://doi.org/10.1103/physrevlett.134.160403

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