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 zero-temperature or infinite-temperature properties and, therefore, can be properly described by the corresponding equilibrium state.

Figure 1

Time evolution of (a, c) the impurity spin polarization and (b, d) the spin density of the fermionic bath in a period for several choices of local magnetic field intensity $h$ ($h=10\mathrm{\Delta }$, blue solid line; $h=2.5\mathrm{\Delta }$, red dashed line; $h=0.625\mathrm{\Delta }$, yellow dash-dotted line). (a, b) $\tau =10/\mathrm{\Delta }$; (c, d) $\tau =0.3125/\mathrm{\Delta }$.

Figure 2

Time-averaged quantities as a function of the local magnetic field intensity $h$: time-averaged impurity spin polarization $\overline{S^z}$ (blue solid line), variance $\mathrm{\Delta }{S}^z$ (red dashed line), and work $W$ (yellow dash-dotted line).

Figure 3

Time evolution of (a, c) the impurity spin polarization and (b, d) the spin density of the fermionic bath in a half of the driving period for several choices of local magnetic field $h$ ($h=10\overline{\mathrm{\Delta }}$, blue solid line; $h=2.5\overline{\mathrm{\Delta }}$, red dashed line; $h=0.625\overline{\mathrm{\Delta }}$, yellow dash-dotted line). (a, b) $\tau =20/\overline{\mathrm{\Delta }}$; (c, d) $\tau =0.625/\overline{\mathrm{\Delta }}$.