We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized spectral representation ansatz by including high-order vertex corrections and its numerical analytic continuation procedures. The differential conductance calculations agree accurately with available data from other nonequilibrium transport theories. It is verified that, at finite source-drain voltage, the Kondo resonance is destroyed at bias comparable to the Kondo temperature. Calculated scaling coefficients of differential conductance for zero-bias anomaly fall within the range of experimental estimates.
We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized spectral representation ansatz by including high-order vertex corrections and its numerical analytic continuation procedures. The differential conductance calculations agree accurately with available data from other nonequilibrium transport theories. It is verified that, at finite source-drain voltage, the Kondo resonance is destroyed at bias comparable to the Kondo temperature. Calculated scaling coefficients of differential conductance for zero-bias anomaly fall within the range of experimental estimates.
Recently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ continuous-time quantum Monte-Carlo solvers to calculate accurate imaginary time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.
We discuss the formal relationship between the real-time Keldysh and imaginary-time theory for nonequilibrium in quantum dot systems. The latter can be reformulated using the recently proposed Matsubara-voltage approach. We establish general conditions for correct analytic continuation procedure on physical observables, and apply the technique to the calculation of static quantities in steady-state nonequilibrium for a quantum dot subject to a finite bias voltage and external magnetic field. Limitations of the Matsubara voltage approach are also pointed out.
In a recent work [17] Han and Heary introduced a formalism approaching steady-state quantum transport through mesoscopic structures which maps the non-equilibrium problem onto a family of auxiliary equilibrium quantum impurity systems by introducing imaginary voltages. We apply continuous-time quantum Monte-Carlo solvers to obtain precise and unbiased imaginary-time data for these auxiliary models. Physical observables are obtained by an analytical continuation in both Matsubara frequency and complexified voltage using a Maximum Entropy Method (MEM). The MEM is introduced by means of a kernel function compatible with the analytical structure of the theory. While it remains a yet challenging task to obtain reliable spectral functions, this unbiased procedure seems to indicate that the formalism yields results which are compatible with those of other methods.
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.
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.