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The time-dependent numerical renormalization group method (TDNRG) [Anders etal., Phys. Rev. Lett. {\bf 95}, 196801 (2005)] was recently generalized tomultiple quenches and arbitrary finite temperatures [Nghiem et al., Phys. Rev.B {\bf 89}, 075118 (2014)] by using the full density matrix approach[Weichselbaum et al., Phys. Rev. Lett. {\bf 99}, 076402 (2007)]. In this paper,we numerically implement this formalism to study the response of a quantumimpurity system to a general pulse and periodic driving which are approximatedby a sufficient number of quenches. We show how the NRG approximation affectsthe trace of the projected density matrices and the continuity of thetime-evolution of a local observable. For the general pulse case, the localobservable in the long-time limit exhibits a dependence on the switch-on time,the time interval between the first and last quenches, as well as on the pulseshape. In particular, the long-time limit is improved for longer switch-ontimes and smoother pulses. This lends support to our earlier suggestion thatthe long-time limit of observables can be improved by replacing a sudden largequench by a sequence of smaller ones acting over a finite time-interval: longerswitch-on times and smoother pulses, i.e., increased adiabaticity, favorrelaxation of the system to its correct thermodynamic long-time limit. For thecase of periodic driving, we compare the TDNRG results to exact analytic onesfor the non-interacting resonant level model, finding better agreement at shortto intermediate time scales in the case of smoother driving. Finally, wedemonstrate the validity of the multiple-quench TDNRG formalism for arbitrarytemperatures by studying the time-evolution of the occupation number in theAnderson impurity model in response to a periodic switching of the local levelfrom the mixed valence to the Kondo regime at finite temperatures.

Time-Dependent Numerical Renormalization Group Method for Multiple Quenches: Application to General Pulses and Periodic Driving