Time-Dependent Numerical Renormalization Group Method for Multiple Quenches: Application to General Pulses and Periodic Driving
arXiv:1406.3444 · doi:10.1103/PhysRevB.90.035129
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.
12 pages and 8 figures
References in corpus (22)
- Continuous-time Monte Carlo methods for quantum impurity models
- The numerical renormalization group method for quantum impurity systems
- Real time evolution using the density matrix renormalization group
- Driven coherent oscillations of a single electron spin in a quantum dot
- The Kernel Polynomial Method
- Interaction Quench in the Hubbard model
- Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
- Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
- Real-time path integral approach to nonequilibrium many-body quantum system
- Theoretical description of time-resolved photoemission spectroscopy: application to pump-probe experiments
- Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
- Thermoelectric transport through strongly correlated quantum dots
- On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
- Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
- Iterative real-time path integral approach to nonequilibrium quantum transport
- A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
- Kondo decoherence: finding the right spin model for iron impurities in gold and silver
- Theory of time-resolved optical spectroscopy on correlated electron systems
- Fermionic superoperators for zero-temperature non-linear transport: real-time perturbation theory and renormalization group for Anderson quantum dots
- Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
- Full density matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model
- Quench dynamics of correlated quantum dots