Numerical Renormalization Group Analysis of Interacting Quantum Dots

Wilson’s Numerical Renormalization Group (NRG) is so far the only nonperturbative technique that can reliably access low–energy properties of quantum impurity systems. We present a recent extension of the method, the DM–NRG, which yields highly accurate results for dynamical quantities at arbitrary frequencies and temperatures. As an application, we determine the spectrum of a quantum dot in an external magnetic field. Furthermore, we discuss magnetic impurities with orbital degeneracy, which have been inferred in recent experiments on quantum dots in an Aharonov-Bohm geometry. It is demonstrated that for spinless electrons, interference between neighbouring levels sets the low–energy scale of the system. Switching on an external field leads to a remarkable crossover into a regime dominated by orbital Kondo screening. We predict that the broadening–induced level splitting should be clearly visible in measurements of the optical absorption power. A more general model including the electron spin is studied within an extended two-band NRG procedure. We observe competition between interference and Kondo screening, similar to the situation in two-impurity models (RKKY).