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arXiv:0808.0442 · Physical Review B

Transient dynamics of the Anderson impurity model out of equilibrium

Thomas L. Schmidt, Philipp Werner, Lothar Mühlbacher, A. Komnik

Published Dec 10, 2008• 122 citations
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Abstract

We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.

DOI
10.1103/physrevb.78.235110

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We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.
One of the main open problems in the field of transport in strongly interacting nanostructures is the understanding of currents beyond the linear response regime. In this work, we consider the single-impurity Anderson model and use the adaptive time-dependent density matrix renormalization group method to compute real-time currents out of equilibrium. We first focus on the particle-hole symmetric point where Kondo correlations are the strongest and then extend the study of the nonequilibrium transport to the mixed-valence regime. As a main result, we present accurate data for the current-voltage characteristics of this model.
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We extend the general formalism discussed in the previous paper (A. B. Culver and N. Andrei, [Phys. Rev. B 103, 195106 (2021)]) to two models with charge fluctuations: the interacting resonant level model and the Anderson impurity model. In the interacting resonant level model, we find the exact time-evolving wavefunction and calculate the steady-state impurity occupancy to leading order in the interaction. In the Anderson impurity model, we find the nonequilibrium steady state for small or large Coulomb repulsion UUU, and we find that the steady-state current to leading order in UUU agrees with a Keldysh perturbation theory calculation.
We analyze the spectrum of the electric-current autocorrelation function (noise power) in the Anderson impurity model biased by a finite transport voltage. Special emphasis is placed on the interplay of nonequilibrium effects and electron-electron interactions. Analytic results are presented for a perturbation expansion in the interaction strength UUU. Compared to the noninteracting setup we find a suppression of noise for finite frequencies in equilibrium and an amplification in nonequilibrium. Furthermore, we use a diagrammatic resummation scheme to obtain nonperturbative results in the regime of intermediate UUU. At finite voltage, the noise spectrum shows sharp peaks at positions related to the Kondo temperature instead of the voltage.
The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real-time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.
We study the interacting, symmetrically coupled single impurity Anderson model. By employing the nonequilibrium Green's function formalism, we reach an exact relationship between the steady-state charge current flowing through the impurity (dot) and its occupation. We argue that the steady-state current-occupation relation can be used to assess the consistency of simulation techniques and identify spurious transport phenomena. We test this relation in two different model variants: First, we study the Anderson-Holstein model in the strong electron-vibration coupling limit using the polaronic quantum master equation method. We find that the current-occupation relation is violated numerically in standard calculations, with simulations bringing up incorrect transport effects. Using a numerical procedure, we resolve the problem efficiently. Second, we simulate the Anderson model with electron-electron interaction on the dot using a deterministic numerically exact time-evolution scheme. Here, we observe that the current-occupation relation is satisfied in the steady-state limit-even before results converge to the exact limit.