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 (2
014)] 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.
We consider iron impurities in the noble metals gold and silver and compare experimental data for the resistivity and decoherence rate to numerical renormalization group results. By exploiting non-Abelian symmetries we show improved numerical data fo
r both quantities as compared to previous calculations [Costi et al., Phys. Rev. Lett. 102, 056802 (2009)], using the discarded weight as criterion to reliably judge the quality of convergence of the numerical data. In addition we also carry out finite-temperature calculations for the magnetoresistivity of fully screened Kondo models with S = 1/2, 1 and 3/2, and compare the results with available measurements for iron in silver, finding excellent agreement between theory and experiment for the spin-3/2 three-channel Kondo model. This lends additional support to the conclusion of Costi et al. that the latter model provides a good effective description of the Kondo physics of iron impurities in gold and silver.
We investigate the thermoelectric properties of PbTe doped with a small concentration $x$ of Tl impurities acting as acceptors and described by Anderson impurities with negative on-site (effective) interaction. The resulting charge Kondo effect natur
ally accounts for a number of the low temperature anomalies in this system, including the unusual doping dependence of the carrier concentration, the Fermi level pinning and the self-compensation effect. The Kondo anomalies in the low temperature resistivity at temperatures $Tleq 10, {rm K}$ and the $x$-dependence of the residual resistivity are also in good agreement with experiment. Our model also captures the qualitative aspects of the thermopower at higher temperatures $T>300, {rm K}$ for high dopings ($x>0.6%$) where transport is expected to be largely dominated by carriers in the heavy hole band of PbTe.
We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation
for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{rm imp}$, to be calculated accurately from local static correlation functions; specifically via $C_{rm imp}=frac{partial E_{rm ionic}}{partial T} + 1/2frac{partial E_{rm hyb}}{partial T}$, where $E_{rm ionic}$ and $E_{rm hyb}$ are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to $C_{rm imp}$. For the non-degenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The new approach could also be of interest within other impurity solvers, e.g., within quantum Monte Carlo techniques.
We investigate with the aid of numerical renormalization group techniques the thermoelectric properties of a molecular quantum dot described by the negative-U Anderson model. We show that the charge Kondo effect provides a mechanism for enhanced ther
moelectric power via a correlation induced asymmetry in the spectral function close to the Fermi level. We show that this effect results in a dramatic enhancement of the Kondo induced peak in the thermopower of negative-U systems with Seebeck coefficients exceeding 50$mu V/K$ over a wide range of gate voltages.
The ability to make electrical contact to single molecules creates opportunities to examine fundamental processes governing electron flow on the smallest possible length scales. We report experiments in which we controllably stretch individual cobalt
complexes having spin S = 1, while simultaneously measuring current flow through the molecule. The molecules spin states and magnetic anisotropy were manipulated in the absence of a magnetic field by modification of the molecular symmetry. This control enabled quantitative studies of the underscreened Kondo effect, in which conduction electrons only partially compensate the molecular spin. Our findings demonstrate a mechanism of spin control in single-molecule devices and establish that they can serve as model systems for making precision tests of correlated-electron theories.
We exploit the decoherence of electrons due to magnetic impurities, studied via weak localization, to resolve a longstanding question concerning the classic Kondo systems of Fe impurities in the noble metals gold and silver: which Kondo-type model yi
elds a realistic description of the relevant multiple bands, spin and orbital degrees of freedom? Previous studies suggest a fully screened spin $S$ Kondo model, but the value of $S$ remained ambiguous. We perform density functional theory calculations that suggest $S = 3/2$. We also compare previous and new measurements of both the resistivity and decoherence rate in quasi 1-dimensional wires to numerical renormalization group predictions for $S=1/2,1$ and 3/2, finding excellent agreement for $S=3/2$.
