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We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor K (t) analytically for a minimal Floquet circuit model that has a U (1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate K (t) 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" tₓ₇ demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for K (t) at t≲tₓ₇. We also report numerical results for K (t) in a generic Floquet spin model, which are consistent with these analytic predictions.
Friedman et al. (Fri,) studied this question.
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