Transport Through Correlated Quantum Dots -- A Functional Renormalization Group Approach

We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries. A detailed derivation of a truncated set of RG flow equations that requires only basic knowledge of the functional integral approach to many-particle physics is given. Using fRG we study linear-response transport properties of a variety of quantum dots in the zero-temperature limit. For parallel geometries, we observe a generic crossover from mesoscopic to universal behaviour of the transmission phase if the single-particle level spacing is gradually decreased. We tackle a couple of well-known systems (the SIAM, the side-coupled geometry and short Hubbard chains), showing that the fRG correctly captures Kondo physics. We make use of the little computational resources required to scan the whole parameter space of these systems, partly uncovering new physics. The high accuracy of the fRG is demonstrated by extensive comparisons with NRG data.