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We investigate the time evolution of the Kondo resonance in response to a quench by applying the time-dependent numerical renormalization group (TDNRG) approach to the Anderson impurity model in the strong correlation limit. For this purpose, we derive within TDNRG a numerically tractable expression for the retarded two-time nonequilibrium Green function $G(t+t,t)$, and its associated time-dependent spectral function, $A(omega,t)$, for times $t$ both before and after the quench. Quenches from both mixed valence and Kondo correlated initial states to Kondo correlated final states are considered. For both cases, we find that the Kondo resonance in the zero temperature spectral function, a preformed version of which is evident at very short times $tto 0^{+}$, only fully develops at very long times $tgtrsim 1/T_{rm K}$, where $T_{rm K}$ is the Kondo temperature of the final state. In contrast, the final state satellite peaks develop on a fast time scale $1/Gamma$ during the time interval $-1/Gamma lesssim t lesssim +1/Gamma$, where $Gamma$ is the hybridization strength. Initial and final state spectral functions are recovered in the limits $trightarrow -infty$ and $trightarrow +infty$, respectively. Our formulation of two-time nonequilibrium Green functions within TDNRG provides a first step towards using this method as an impurity solver within nonequilibrium dynamical mean field theory.
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We investigate several definitions of the time-dependent spectral function $A(omega,t)$ of the Anderson impurity model following a quench and within the time-dependent numerical renormalization group method. In terms of the two-time retarded Green function $G^r(t_1,t_2)$, the definitions differ in the choice of the time variable $t$ with respect to $t_1$ and/or $t_2$. In a previous study [Nghiem {it et al.} Phys. Rev. Lett. 119, 156601 (2017)], we investigated the spectral function, obtained from the Fourier transform of ${rm Im}[G^r(t_1,t_2)]$ w.r.t. the time difference $t=t_1-t_2$, with $t=t_2$. Here, we derivie expressions for the retarded Green function for the choices $t=t_1$ and the average time $t=(t_1+t_2)/2$, within the TDNRG approach. We compare and contrast the resulting $A(omega,t)$ for the different choices of time reference. Expressions for the lesser, greater and advanced Green functions are also derived within TDNRG for all choices of time reference. The average time lesser Green function $G^<(omega,t)$ is particularly interesting, as it determines the time-dependent occupied density of states $N(omega,t)=G^<(omega,t)/(2pi i)$, a quantity that determines the photoemission current in time-resolved pump-probe photoemission spectroscopy. We present calculations for $N(omega,t)$ for the Anderson model following a quench, and discuss the resulting time evolution of the spectral features, such as the Kondo resonance and high-energy peaks. We also discuss the issue of thermalization at long times for $N(omega,t)$. Finally, we use the results for $N(omega,t)$ to calculate the time-resolved photoemission current for the Anderson model following a quench (acting as the pump) and study the different behaviors that can be observed for different resolution times of a Gaussian probe pulse.
Using the adaptive time-dependent density matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.
We find the statistical weight of excitations at long times following a quench in the Kondo problem. The weights computed are directly related to the overlap between initial and final states that are, respectively, states close to the Kondo ground state and states close to the normal metal ground state. The overlap is computed making use of the Slavnov approach, whereby a functional representation method is adopted, in order to obtain definite expressions.
In the previous paper, we found a series expression for the average electric current following a quench in the nonequilibrium Kondo model driven by a bias voltage. Here, we evaluate the steady state current in the regimes of strong and weak coupling. We obtain the standard leading order results in the usual weak antiferromagnetic regime, and we also find a new universal regime of strong ferromagnetic coupling with Kondo temperature $T_K = D e^{frac{3pi^2}{8} rho J}$. In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.
We study nonequilibrium thermoelectric transport properties of a correlated impurity connected to two leads for temperatures below the Kondo scale. At finite bias, for which a current flows across the leads, we investigate the differential response of the current to a temperature gradient. In particular, we compare the influence of a bias voltage and of a finite temperature on this thermoelectric response. This is of interest from a fundamental point of view to better understand the two different decoherence mechanisms produced by a bias voltage and by temperature. Our results show that in this respect the thermoelectric response behaves differently from the electric conductance. In particular, while the latter displays a similar qualitative behavior as a function of voltage and temperature, both in theoretical and experimental investigations, qualitative differences occur in the case of the thermoelectric response. In order to understand this effect, we analyze the different contributions in connection to the behavior of the impurity spectral function versus temperature. Especially in the regime of strong interactions and large enough bias voltages we obtain a simple picture based on the asymmetric suppression or enhancement of the split Kondo peaks as a function of the temperature gradient. Besides the academic interest, these studies could additionally provide valuable information to assess the applicability of quantum dot devices as responsive nanoscale temperature sensors.
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