We investigate the Kondo model with time-dependent couplings that areperiodically switched on and off. On the Toulouse line we derive exactanalytical results for the spin dynamics in the steady state that builds upafter an infinite number of switching periods. Remarkably, the algebraic longtime behavior of the spin-spin correlation function remains completelyunaffected by the driving. In the limit of slow driving the dynamics becomeequivalent to that of a single interaction quench. In the limit of fast drivingone can show that the steady state cannot be described by some effectiveequilibrium Hamiltonian since a naive implementation of the Trotter formulagives wrong results. As a consequence, the steady state in the limit of fastswitching serves as an example for the emergence of new quantum states notaccessible in equilibrium.
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