The Kondo Effect in Yb: Examining the Competition of Magnetic and Non-Magnetic Scattering in Luttinger Liquids

173-Ytterbium offers an ideal platform to study the Kondo effect. With current experimental techniques involving optical tweezers and state selective trapping potentials it is possible to create isolated impurities interacting with a sea of conducting fermions formed from atoms hopping on an optical lattice. The only caveat, however, is that in Ytterbium systems the impurity will induce both a spin-dependent and density-dependent interaction. While the spin-dependent interaction can lead to the Kondo effect at low-temperatures, the density-dependent interaction tends to push fermions away from the impurity and inhibits the Kondo effect. In this talk we investigate a one-dimensional fermi gases of Yb atoms coupled to an isolated impurity through magnetic and non-magnetic interactions. We show using a renormalization group calculation within Luttinger liquid theory that the non-magnetic scattering impedes the Kondo temperature. This result is supported by DMRG simulations and provide us with insight under what conditions the Kondo effect can be seen in current experiments.