Random matrix spectral form factor in kicked interacting fermionic chains

We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle-number conservation [U (1 )] symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless time which scales with the size L as O (L²) , or O (L⁰) , in the presence, or absence, of U (1 ) symmetry, respectively. Using a random phase assumption which essentially requires a long-range nature of the interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless X X X , or gapped X X Z , spin-1/2 chain Hamiltonian.