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In periodically-driven quantum systems, resonances can induce exoticnonequilibrium behavior and new phases of matter without static analog. Wereport on the emergence of fractional and integer resonances in a broad classof many-body Hamiltonians with a modulated hopping with a frequency that iseither a fraction or an integer of the on-site interaction. We contend thatthere is a fundamental difference between these resonances when interactionsbring the system to a Floquet prethermal state. Second-order processes dominatethe dynamics in the fractional resonance case, leading to less entanglement andmore localized quantum states than in the integer resonance case dominated byfirst-order processes. We demonstrate the dominating emergence of fractionalresonances using the Magnus expansion of the effective Hamiltonian and quantifytheir effects on the many-body dynamics via quantum states' von Neumann entropyand Loschmidt echo. Our findings reveal novel features of the nonequilibriumquantum many-body system, such as the coexistence of Floquet prethermalizationand localization, that may allow to development of quantum memories for quantumtechnologies and quantum information processing.

Fractional resonances and prethermal states in Floquet systems