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Within the recently introduced auxiliary master equation approach it ispossible to address steady state properties of strongly correlated impuritymodels, small molecules or clusters efficiently and with high accuracy. It isparticularly suited for dynamical mean field theory in the nonequilibrium aswell as in the equilibrium case. The method is based on the solution of anauxiliary open quantum system, which can be made quickly equivalent to theoriginal impurity problem. In its first implementation a Krylov space methodwas employed. Here, we aim at extending the capabilities of the approach byadopting matrix product states for the solution of the corresponding auxiliaryquantum master equation. This allows for a drastic increase in accuracy andpermits us to access the Kondo regime for large values of the interaction. Inparticular, we investigate the nonequilibrium steady state of a single impurityAnderson model and focus on the spectral properties for temperatures T belowthe Kondo temperature T_K and for small bias voltages phi. For the two casesconsidered, with T=T_K/4 and T=T_K/10 we find a clear splitting of the Kondoresonance into a two-peak structure for phi close above T_K. In the equilibriumcase (phi=0) and for T=T_K/4, the obtained spectral function essentiallycoincides with the one from numerical renormalization group.

Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model