  We calculate steady-state properties of a strongly correlated quantum dot
under voltage bias by means of non-equilibrium Cluster Perturbation Theory and
the non-equilibrium Variational Cluster Approach, respectively. Results for the
steady-state current are benchmarked against data from accurate Matrix Product
State based time evolution. We show that for low to medium interaction
strength, non-equilibrium Cluster Perturbation Theory already yields good
results, while for higher interaction strength the self-consistent feedback of
the non-equilibrium Variational Cluster Approach significantly enhances the
accuracy. We report the current-voltage characteristics for different
interaction strengths. Furthermore we investigate the non-equilibrium local
density of states of the quantum dot and illustrate that within the variational
approach a linear splitting and broadening of the Kondo resonance is predicted
which depends on interaction strength. Calculations with applied gate voltage,
away from particle hole symmetry, reveal that the maximum current is reached at
the crossover from the Kondo regime to the doubly-occupied or empty quantum
dot. Obtained stability diagrams compare very well to recent experimental data
[Phys. Rev. B, 84, 245316 (2011)].
