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 O(L2), or O(L0), 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.Comment: 6 pages, 1 figur