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.
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.
We study equilibrium and nonequilibrium properties of the single-impurity Anderson model with a power-law pseudogap in the density of states. In equilibrium, the model is known to display a quantum phase transition from a generalized Kondo to a local moment phase. In the present work, we focus on the extension of these phases beyond equilibrium, i.e., under the influence of a bias voltage. Within the auxiliary master equation approach combined with a scheme based on matrix product states (MPS) we are able to directly address the current-carrying steady state. Starting with the equilibrium situation, we first corroborate our results by comparing to a direct numerical evaluation of ground-state spectral properties of the system by MPS. Here, a scheme to locate the phase boundary by extrapolating the power-law exponent of the self energy produces a very good agreement with previous results obtained by the numerical renormalization group. Our nonequilibrium study as a function of the applied bias voltage is then carried out for two points on either side of the phase boundary. In the Kondo regime the resonance in the spectral function is split as a function of the increasing bias voltage. The local moment regime, instead, displays a dip in the spectrum near the position of the chemical potentials. Similar features are observed in the corresponding self energies. The Kondo split peaks approximately obey a power-law behavior as a function of frequency whose exponents depend only slightly on voltage. Finally, the differential conductance in the Kondo regime shows a peculiar maximum at finite voltages, whose height, however, is below the accuracy level.
Within the recently introduced auxiliary master equation approach it is possible to address steady state properties of strongly correlated impurity models, small molecules or clusters efficiently and with high accuracy. It is particularly suited for dynamical mean field theory in the nonequilibrium as well as in the equilibrium case. The method is based on the solution of an auxiliary open quantum system, which can be made quickly equivalent to the original impurity problem. In its first implementation a Krylov space method was employed. Here, we aim at extending the capabilities of the approach by adopting matrix product states for the solution of the corresponding auxiliary quantum master equation. This allows for a drastic increase in accuracy and permits us to access the Kondo regime for large values of the interaction. In particular, we investigate the nonequilibrium steady state of a single impurity Anderson model and focus on the spectral properties for temperatures T below the Kondo temperature T_K and for small bias voltages phi. For the two cases considered, with T=T_K/4 and T=T_K/10 we find a clear splitting of the Kondo resonance into a two-peak structure for phi close above T_K. In the equilibrium case (phi=0) and for T=T_K/4, the obtained spectral function essentially coincides with the one from numerical renormalization group.
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.
We present improvements of a recently introduced numerical method [E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)] to compute steady-state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a nonequilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the nonequilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, Nb uncorrelated bath sites, and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of Nb than previously in DMFT. This increases the accuracy of the results and is crucial for a correct description of the physical behavior of the system in the relevant parameter range including a semiquantitative description of the Kondo regime. To illustrate the approach, we consider a monoatomic layer of correlated orbitals, described by the single-band Hubbard model, attached to two metallic leads. The nonequilibrium situation is driven by a bias voltage applied to the leads. For this system, we investigate the spectral function and the steady-state current-voltage characteristics in the weakly as well as in the strongly interacting limit. In particular, we investigate the nonequilibrium behavior of quasiparticle excitations within the Mott gap of the correlated layer. We find for low-bias voltage Kondo-type behavior in the vicinity of the insulating phase. In particular, we observe a splitting of the Kondo resonance as a function of the bias voltage.
Using different techniques, and Fermi-liquid relationships, we calculate the variation with the applied magnetic field (up to second order) of the zero-temperature equilibrium conductance through a quantum dot described by the impurity Anderson model. We focus on the strong-coupling limit $U\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$, where U is the Coulomb repulsion and $\mathrm{\ensuremath{\Delta}}$ is half the resonant-level width, and consider several values of the dot level energy Ed, ranging from the Kondo regime ${\ensuremath{\epsilon}}_{F}\ensuremath{-}{E}_{d}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$ to the intermediate-valence regime ${\ensuremath{\epsilon}}_{F}\ensuremath{-}{E}_{d}\ensuremath{\sim}\mathrm{\ensuremath{\Delta}}$, where ${\ensuremath{\epsilon}}_{F}$ is the Fermi energy. We have mainly used the density-matrix renormalization group (DMRG) and the numerical renormalization group (NRG) combined with renormalized perturbation theory (RPT). Results for the dot occupancy and magnetic susceptibility from the DMRG and NRG+RPT are compared with the corresponding Bethe ansatz results for $U\ensuremath{\rightarrow}\ensuremath{\infty}$, showing an excellent agreement once Ed is renormalized by a constant Haldane shift. For $U<3\mathrm{\ensuremath{\Delta}}$ a simple perturbative approach in U agrees very well with the other methods. The conductance decreases with the applied magnetic field for dot occupancies ${n}_{d}\ensuremath{\sim}1$ and increases for ${n}_{d}\ensuremath{\sim}0.5$ or ${n}_{d}\ensuremath{\sim}1.5$ regardless of the value of U. We also relate the energy scale for the magnetic-field dependence of the conductance with the width of the low-energy peak in the spectral density of the dot.
We present a numerical method for the study of correlated quantum impurity problems out of equilibrium, which is particularly suited to address steady-state properties within dynamical mean field theory. The approach, recently introduced by Arrigoni et al. [Phys. Rev. Lett. 110, 086403 (2013)], is based upon a mapping of the original impurity problem onto an auxiliary open quantum system, consisting of the interacting impurity coupled to bath sites as well as to a Markovian environment. The dynamics of the auxiliary system is governed by a Lindblad master equation whose parameters are used to optimize the mapping. The accuracy of the results can be readily estimated and systematically improved by increasing the number of auxiliary bath sites, or by introducing a linear correction. Here, we focus on a detailed discussion of the proposed approach including technical remarks. To solve for the Green's functions of the auxiliary impurity problem, a non-Hermitian Lanczos diagonalization is applied. As a benchmark, results for the steady-state current-voltage characteristics of the single-impurity Anderson model are presented. Furthermore, the bias dependence of the single-particle spectral function and the splitting of the Kondo resonance are discussed. In its present form, the method is fast, efficient, and features a controlled accuracy.