  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/Ehrenfest time which scales with
the size $L$ as ${\cal O}(L^2)$, or ${\cal O}(L^0)$, in the presence, or
absence of $U(1)$ symmetry, respectively. Using random phase assumption which
essentially requires long-range nature of 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 $XXX$, or gapped $XXZ$, spin-1/2 chain
Hamiltonian.
