Electronic correlation in nanoscale junctions: Comparison of the GW approximation to a numerically exact solution of the single-impurity Anderson model

The impact of electronic correlation in nanoscale junctions, e.g. formed by single molecules, is analyzed using the single-impurity Anderson model. Numerically exact Quantum Monte Carlo calculations are performed to map out the orbital filling, linear response conductance and spectral function as a function of the Coulomb interaction strength and the impurity level position. These numerical results form a benchmark against which approximate, but more broadly applicable, approaches to include electronic correlation in transport can be compared. As an example, the self consistent GW approximation has been implemented for the Anderson model and the results compared to this benchmark. For weak coupling or for level positions such that the impurity is either nearly empty or nearly full, the GW approximation is found to be accurate. However, for intermediate or strong coupling, the GW approximation does not properly represent the impact of spin or charge fluctuations. Neither the spectral function nor the linear response conductance are accurately given across the Coulomb blockade plateau and well into the mixed valence regimes.