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Mathematical Physics Seminar

Quantum Impurity in Interacting Environments

Natan Andrei - Rutgers University

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.

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