| الملخص: | <p>We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor <em>K</em>(<em>t</em>) analytically for a minimal Floquet circuit model that has a <em>U</em>(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate <em>K</em>(<em>t</em>) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the “Thouless time” <em>t</em><sub>Th</sub> demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for <em>K</em>(<em>t</em>) at <em>t</em>≲<em>t</em><sub>Th</sub>. We also report numerical results for <em>K</em>(<em>t</em>) in a generic Floquet spin model, which are consistent with these analytic predictions.</p>
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