Kondo effect under extreme conditions: testing the limits of the Numerical Renormalization Group

Abstract

The study of physical phenomena under extreme conditions (very low temperatures, for example) has historically shown the potential to uncover unexpected states in Condensed matter Physics, at the same time, it poses a stiff challenge to both experimental and theoretical research techniques. One celebrated example was the discovery of superconductivity when it became possible to liquefy helium and thus perform resistivity measurements at temperatures of a few Kelvin. Following this approach, in this Thesis we study the Kondo effect under two extreme conditions: (i) systems where the metallic host density of states presents a strong divergency near the Fermi energy; (ii) T-shape double quantum dot (DQD) systems, where the energy scale of interest spans 20 orders of magnitude. Both systems were studied using the Numerical Renormalization Group (NRG) method. In (i), we obtained that relatively soft divergencies, of the $\omega^{{-1}/{2}}$-type, generate a series of many-body bound-states with peculiar properties. We thus believe that stronger divergencies (associated to flat bands, for example) have the potential to uncover additional surprises. As to the DQD system, we obtained results that allow us to guide the experimentalists on how to tune the DQD characteristics in order to clearly distinguish two regimes with very different properties, viz., the two-stage Kondo regime and the molecular regime. To analyze the Kondo effect in these so-called extreme conditions (strong host DOS divergencies and extreme energy scale variation) it was necessary to force the NRG into high-demand scenarios, pushing its parameters to extreme values.