Abstract
Phys. Rev. B 97, 155426 (2018) A quantum impurity attached to an interacting quantum wire gives rise to an
array of of new phenomena. Using Bethe Ansatz we solve exactly models
describing two geometries of a quantum dot coupled to an interacting quantum
wire: a quantum dot that is (i) side-coupled and (ii) embedded in a Luttinger
liquid. We find the eigenstates and determine the spectrum through the Bethe
Ansatz equations. Using this we derive exact expressions for the ground state
dot occupation. The thermodynamics are then studied using the thermodynamics
Bethe Ansatz equations. It is shown that at low energies the dot becomes fully
hybridized and acts as a backscattering impurity or tunnel junction depending
on the geometry and furthermore that the two geometries are related by changing
the sign of the interactions. Although remaining strongly coupled for all
values of the interaction in the wire, there exists competition between the
tunneling and backscattering leading to a suppression or enhancement of the dot
occupation depending on the sign of the bulk interactions.