Resonant fragility and nonresonant robustness of Floquet eigenstates in kicked spin systems

In classical physics, a key consequence of the Kolmogorov-Arnold-Moser (KAM) and the Poincaré-Birkhoff theorems is that invariant tori of integrable Hamiltonians with nonresonant frequencies survive sufficiently small nonintegrable perturbations as smooth deformations, whereas resonant tori are generically destroyed by breaking into elliptic and hyperbolic periodic orbits. In this contribution, we identify a quantum analog of this distinct sensitivity for 1-degree-of-freedom spin Hamiltonians subject to periodic instantaneous kicks. After detecting quantum signatures of resonances in the participation ratio and in the quasiprobability phase-space distribution of Floquet eigenstates of the perturbed Hamiltonian, we show that eigenstates of the unperturbed Hamiltonian exhibit greater sensitivity against the perturbation when they satisfy a resonant condition. The sensitivity is quantified through the fidelity between perturbed and unperturbed eigenstates. This distinct sensitivity becomes increasingly pronounced as the system size grows. Our findings are supported by numerical results and insights from analytical calculations based on unitary perturbation theory. Since the resonance conditions are set by commensurability with the driving period, this distinct sensitivity may persist in broader classes of periodically driven systems beyond kicked models, providing a preliminary step toward identifying quantum signatures of the classical breaking of resonant tori.