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

TL;DR

This paper extends the time-dependent numerical renormalization group method to multiple quenches and applies it to analyze quantum impurity systems under general pulses and periodic driving, highlighting improved long-time behavior with smoother, longer switch-on times.

Contribution

The paper implements a generalized multiple-quench TDNRG formalism for arbitrary temperatures and demonstrates its effectiveness in modeling complex pulse shapes and periodic driving in quantum impurity systems.

Findings

Longer switch-on times and smoother pulses improve long-time observable limits.

The method accurately captures system response to general pulses and periodic driving.

Better agreement with exact solutions at short to intermediate times for smoother driving.

Abstract

The time-dependent numerical renormalization group method (TDNRG) [Anders et al., Phys. Rev. Lett. {\bf 95}, 196801 (2005)] was recently generalized to multiple 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 quantum impurity system to a general pulse and periodic driving which are approximated by a sufficient number of quenches. We show how the NRG approximation affects the trace of the projected density matrices and the continuity of the time-evolution of a local observable. For the general pulse case, the local observable 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 pulse shape. In particular, the long-time limit is improved for longer switch-on times and smoother pulses. This lends support to our earlier suggestion that the long-time limit of observables can be improved by replacing a sudden large quench by a sequence of smaller ones acting over a finite time-interval: longer switch-on times and smoother pulses, i.e., increased adiabaticity, favor relaxation of the system to its correct thermodynamic long-time limit. For the case of periodic driving, we compare the TDNRG results to exact analytic ones for the non-interacting resonant level model, finding better agreement at short to intermediate time scales in the case of smoother driving. Finally, we demonstrate the validity of the multiple-quench TDNRG formalism for arbitrary temperatures by studying the time-evolution of the occupation number in the Anderson impurity model in response to a periodic switching of the local level from the mixed valence to the Kondo regime at finite temperatures.