We present improvements of a recently introduced numerical method [Arrigoni etal, 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 non-equilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the non-equilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, $N_b$ uncorrelated bath sites and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of $N_b$ 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 semi-quantitative 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 non-equilibrium 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 non-equilibrium behavior of quasi-particle excitations within the Mott gap of the correlated layer. We find for low bias voltage Kondo like 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.

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