Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge

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" t_{Th} demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for K(t) at t≲t_{Th}. We also report numerical results for K(t) in a generic Floquet spin model, which are consistent with these analytic predictions.