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Periodically-driven Kondo impurity in nonequilibrium steady states

We study the nonequilibrium dynamics of a periodically-driven anisotropic Kondo impurity model. The periodic time dependence is introduced for a local magnetic field which couples to the impurity spin and also for an in-plane exchange interaction. We obtain the exact results on the time evolution for arbitrary periodic time dependence at the special point in the parameter space known as the Toulouse limit. We first consider a specific case where the local magnetic field is periodically switched on and off. When the driving period is much shorter than the inverse of the Kondo temperature, an intriguing oscillating behavior (resonance phenomenon) emerges in the time average of the impurity spin polarization with increasing the local magnetic field intensity. By taking the high frequency limit of the external driving, we elucidate that the system recovers the translational invariance in time and can be described by a mixture of the zero-temperature and infinite-temperature properties. In certain cases, the system is governed by either the zero-temperature or infinite-temperature properties, and therefore can be properly described by the corresponding equilibrium state.