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We present a numerical method for the study of correlated quantum impurityproblems out of equilibrium, which is particularly suited to address steadystate properties within Dynamical Mean Field Theory. The approach, recentlyintroduced in [Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)], is basedupon a mapping of the original impurity problem onto an auxiliary open quantumsystem, consisting of the interacting impurity coupled to bath sites as well asto a Markovian environment. The dynamics of the auxiliary system is governed bya Lindblad master equation whose parameters are used to optimize the mapping.The accuracy of the results can be readily estimated and systematicallyimproved by increasing the number of auxiliary bath sites, or by introducing alinear correction. Here, we focus on a detailed discussion of the proposedapproach including technical remarks. To solve for the Green's functions of theauxiliary impurity problem, a non-hermitian Lanczos diagonalization is applied.As a benchmark, results for the steady state current-voltage characteristics ofthe single impurity Anderson model are presented. Furthermore, the biasdependence of the single particle spectral function and the splitting of theKondo resonance are discussed. In its present form the method is fast,efficient and features a controlled accuracy.

Auxiliary master equation approach to non-equilibrium correlated impurities