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The emergence of random matrix spectral correlations in interacting quantumsystems is a defining feature of quantum chaos. We study such correlations interms of the spectral form factor and its moments in interacting chaotic few-and many-body systems, modeled by suitable random-matrix ensembles. We obtainthe spectral form factor exactly for large Hilbert space dimension.Extrapolating those results to finite Hilbert space dimension we find auniversal transition from the non-interacting to the strongly interacting case,which can be described as a simple combination of these two limits. Thistransition is governed by a single scaling parameter. In the bipartite case wederive similar results also for all moments of the spectral form factor. Weconfirm our results by extensive numerical studies and demonstrate that theyapply to more realistic systems given by a pair of quantized kicked rotors aswell. Ultimately we complement our analysis by a perturbative approach coveringthe small coupling regime.

Universal spectral correlations in interacting chaotic few-body quantum systems