Correlation effects in transport properties of interacting nanostructures

We discuss how to apply many-body methods to correlated nanoscopic systems, and provide general criteria of validity for a treatment at the dynamical mean field theory (DMFT) approximation level, in which local correlations are taken into account, while nonlocal ones are neglected. In this respect, we consider one of the most difficult cases for DMFT, namely, for a quasi-one-dimensional molecule such as a benzene ring. The comparison against a numerically exact solution shows that nonlocal spatial correlations are relevant only in the limit of weak coupling between the molecule and the metallic leads and of low inter-atomic connectivity, otherwise DMFT provides a quantitative description of the system. As an application we investigate the role of correlations on electronic transport in quantum junctions, and we show that a local Mott-Hubbard crossover is a robust phenomenon in sharp nanoscopic contacts.