Time-dependent numerical renormalization group method for multiple quenches: Application to general pulses and periodic driving

Nghiem, Hoa; Costi, Theodoulos

doi:10.1103/PhysRevB.90.035129

Journal Article

FZJ-2014-04192

Time-dependent numerical renormalization group method for multiple quenches: Application to general pulses and periodic driving

Nghiem, H. (Corresponding author)FZJ* ; Costi, T.FZJ*

2014
APS College Park, Md.

Physical review / B 90(3), 035129 (2014) [10.1103/PhysRevB.90.035129]

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Please use a persistent id in citations: http://hdl.handle.net/2128/7847 doi:10.1103/PhysRevB.90.035129

Abstract: The time-dependent numerical renormalization group method (TDNRG) [Anders et al., Phys. Rev. Lett. 95, 196801 (2005)] was recently generalized to multiple quenches and arbitrary finite temperatures [Nghiem et al., Phys. Rev. B 89, 075118 (2014)] by using the full density matrix approach [Weichselbaum et al., Phys. Rev. Lett. 99, 076402 (2007)]. The formalism rests solely on the numerical renormalization group (NRG) approximation. In this paper, we numerically implement this formalism to study the response of a quantum impurity system to a general pulse and to periodic driving, in which a smooth pulse or a periodic train of pulses is 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. We also investigate the long-time limit of a local observable upon switching from a given initial state to a given final state as a function of both the pulse shape and the switch-on time, finding that this limit is improved for smoother pulse shapes and longer switch-on times. This lends support to our earlier suggestion that the long-time limit of observables, following a quench between a given initial state and a given final state, can be improved by replacing a sudden large and instantaneous 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 the exact analytic ones for the noninteracting resonant level model, finding better agreement at short to intermediate time scales in the case of smoother driving fields. 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 interacting Anderson impurity model in response to a periodic switching of the local level from the mixed valence to the Kondo regime at low, intermediate, and high temperatures.

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