We evaluate the nonequilibrium single-particle Green's functions in the steady state of the interacting resonant level model (IRLM) under the effect of an applied bias voltage. Employing the so-called auxiliary master equation approach, we present accurate nonperturbative results for the nonequilibrium spectral and effective distribution functions, as well as for the current-voltage characteristics. We find a drastic change of these spectral properties between the regimes of low- and high-bias voltages and discuss the relation of these changes to the negative differential conductance (NDC), a prominent feature in the nonequilibrium IRLM. The anomalous evolution of the effective distribution function next to the impurity shown by our calculations suggests a mechanism whereby the impurity gets effectively decoupled from the leads at voltages where the NDC sets in, in agreement with previous renormalization group approaches. This scenario is qualitatively confirmed by a Hartree-Fock treatment of the model.
We evaluate the nonequilibrium single-particle Green's functions in the steady state of the interacting resonant level model (IRLM) under the effect of an applied bias voltage. Employing the so-called auxiliary master equation approach, we present accurate nonperturbative results for the nonequilibrium spectral and effective distribution functions, as well as for the current-voltage characteristics. We find a drastic change of these spectral properties between the regimes of low- and high-bias voltages and discuss the relation of these changes to the negative differential conductance (NDC), a prominent feature in the nonequilibrium IRLM. The anomalous evolution of the effective distribution function next to the impurity shown by our calculations suggests a mechanism whereby the impurity gets effectively decoupled from the leads at voltages where the NDC sets in, in agreement with previous renormalization group approaches. This scenario is qualitatively confirmed by a Hartree-Fock treatment of the model.
We develop a low-order conserving approximation for the interacting resonant-level model (IRLM), and apply it to (i) thermal equilibrium, (ii) nonequilibrium steady state, and (iii) nonequilibrium quench dynamics. Thermal equilibrium is first used to carefully gauge the quality of the approximation by comparing the results with other well-studied methods, and finding good agreement for small values of the interaction. We analytically show that the power-law exponent of the renormalized level width usually derived using renormalization group approaches can also be correctly obtained in our approach in the weak interaction limit. A closed expression for the nonequilibrium steady-state current is derived and analytically and numerically evaluated. We find a negative differential conductance at large voltages, and the exponent of the power-law suppression of the steady-state current is calculated analytically at zero temperature. The response of the system to quenches is investigated for a single lead as well as for two-lead setup at finite voltage bias at particle-hole symmetry using a self-consistent two-times Keldysh Green function approach, and results are presented for the time-dependent current for different bias and contact interaction strength.
Boulat, Saleur and Schmitteckert (BSS) reported results on the full I−V characteristics of the interacting resonant level model (IRLM) exhibiting region with unexpected negative differential conductance (NDC). Using time-dependent density matrix renormalization group complemented with the exact solution performed at a special point (the self-dual point) in the parameter space BSS have shown that at nonzero Coulomb interaction U the current flowing through the impurity level (IL) exhibits a power-law asymptotics as a function of large applied bias voltage. Similar conclusion was earlier reached by Doyon. Even though their results are solid and supported by both analytic and numeric arguments, BSS concluded that "the NDC at large voltage seems a truly nonperturbative behavior, with unclear physical origin". On the contrary, the remarkable physics of NDC can be explained by simple physical arguments and, as we shall show in this Comment, in certain circumstances can be calculated in the framework of perturbation theory.
In this report, we describe a recent development in a Fermi liquid theory for the Kondo effect in quantum dots under a finite bias voltage V. Applying the microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we derive the Ward identities for the Keldysh Green's function, and determine the low-energy behavior of the differential conductance dI/dV exactly up to terms of order (eV)2 for the symmetric Anderson model. These results are deduced from the fact that the Green's function at the impurity site is a functional of a nonequilibrium distribution feff(ω), which at eV=0 coincides with the Fermi function. Furthermore, we provide an alternative description of the low-energy properties using a renormalized perturbation theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is determined by the renormalized free quasiparticles, the distribution function of which is given by feff(ω). The residual interaction between the quasiparticles U, which is defined by the full vertex part at zero frequencies, is taken into account by an expansion in the power series of U. We also discuss the application of the RPT to a high-bias region beyond the Fermi-liquid regime.
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 investigate equilibrium and steady-state nonequilibrium transport properties of a spinless resonant level locally coupled to two conduction bands of width $\ensuremath{\sim}\ensuremath{\Gamma}$ via a Coulomb interaction U and a hybridization ${t}^{\ensuremath{'}}$. In order to study the effects of finite bias voltages beyond linear response, a generalization of the functional renormalization group to Keldysh frequency space is employed. Being mostly unexplored in the context of quantum impurity systems out of equilibrium, we benchmark this method against recently published time-dependent density matrix renormalization group data. We thoroughly investigate the scaling limit $\ensuremath{\Gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$ characterized by the appearance of power laws. Most importantly, at the particle-hole symmetric point the steady-state current decays like $J\ensuremath{\sim}{V}^{\ensuremath{-}{\ensuremath{\alpha}}_{J}}$ as a function of the bias voltage $V⪢{t}^{\ensuremath{'}}$, with an exponent ${\ensuremath{\alpha}}_{J}(U)$ that we calculate to leading order in the Coulomb interaction strength. In contrast, we do not observe a pure power-law (but more complex) current-voltage-relation if the energy ϵ of the resonant level is pinned close to either one of the chemical potentials $\ifmmode\pm\else\textpm\fi{}V/2$.
We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B . We investigate the interplay between the shift ( ) of the Kondo peak in the spin-resolved density of states (DOS) and the one ( ) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as only for . Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.