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

Abstract

In classical systems, the Kolmogorov-Arnold-Moser (KAM) theorem establishes that resonant tori of integrable Hamiltonians are destroyed by any nonintegrable perturbation, whereas nonresonant tori are only deformed up to a finite value of the perturbation parameter. In this contribution, we identify a quantum analog of this differentiated sensitivity for one-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 differentiated 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. Although our analysis focuses on kicked models, the mechanism could be extended to more general periodic drivings, providing a preliminary step toward a quantum counterpart of the classical breaking of resonant tori.