  In periodically-driven quantum systems, resonances can induce exotic
nonequilibrium behavior and new phases of matter without static analog. We
report on the emergence of fractional and integer resonances in a broad class
of many-body Hamiltonians with a modulated hopping with a frequency that is
either a fraction or an integer of the on-site interaction. We contend that
there is a fundamental difference between these resonances when interactions
bring the system to a Floquet prethermal state. Second-order processes dominate
the dynamics in the fractional resonance case, leading to less entanglement and
more localized quantum states than in the integer resonance case dominated by
first-order processes. We demonstrate the dominating emergence of fractional
resonances using the Magnus expansion of the effective Hamiltonian and quantify
their effects on the many-body dynamics via quantum states' von Neumann entropy
and Loschmidt echo. Our findings reveal novel features of the nonequilibrium
quantum many-body system, such as the coexistence of Floquet prethermalization
and localization, that may allow to development of quantum memories for quantum
technologies and quantum information processing.
