Location: HILL 705
Date & time: Thursday, 30 November 2017 at 2:00PM - 3:00PM
Abstract: The Hamilonian of a quantum impurity coupled to a Luttinger Liquid describes a large number of physical systems. It consists of fermions that are left- and right-moving on a line and interacting among themselves via a density-density coupling while scattering off a quantum impurity. Such a system can be realized in many ways. The impurities I will consider will be either a local potential scattering center or quantum dot which are attached to the Luttinger liquid in various geometries – edge coupled, side coupled or body coupled.
I will present exact solutions of the various systems by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. The consistency of the construction is established through a generalized Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe Ansatz equations are derived by means of the Off Diagonal Bethe Ansatz approach. I will derive the spectra of the models for all coupling constant regimes and will calculate the impurity free energy. The high and low energy behavior of the system for both repulsive and attractive interactions will be discussed in detail. Among other things I will show that at low energies the quantum dot becomes fully hybridized and acts as a backscattering impurity or tunnel junction depending on the geometry. Although remaining strongly coupled for all values of the interaction in the Luttinger liquid, there exists competition between the tunneling and the backscattering leading to non Fermi liquid exponents in the specific heat and capacitance of the dot.