Scalar-potential effect in an integrable Kondo model

To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we propose an integrable model of two interacting half-chains coupled with a single magnetic impurity ferromagnetically. It is shown that the scalar potential effectively reconciles the spin dynamics at low temperatures. Generally, there is a competition between the Kondo coupling J and the impurity potential V. When the ferromagnetic Kondo coupling dominates over the impurity potential $(Vl|\mathrm{SJ}|),$ the Furusaki-Nagaosa many-body singlet can be perfectly realized. However, when the impurity potential dominates over the Kondo coupling $(Vg~|\mathrm{SJ}|),$ the fixed point predicted by Furusaki and Nagaosa is unstable and the system must flow to a weak-coupling fixed point. It is also found that the effective moment of the impurity measured from the susceptibility is considerably enlarged by the impurity potential. In addition, some quantum phase transitions driven by the impurity potential are found and the anomaly residual entropy is discussed.