Universal Behavior of Quantum Impurity Scattering in Tomonaga-Luttinger Liquid

Using bosonization and path integral methods, we study general low temperature behavior of non-magnetic and magnetic impurity scattering in Tomonaga-Luttinger liquid, and calculate electron Green function for a general backward scattering potential. We demonstrate that electron density of state near the impurity site is suppressed by the backward scattering, but it mainly remains invariant as far away from the impurity, and at zero temperature the electrons are completely reflected on the impurity site, the system breaks into two subsystems but right- and left-moving electron fields have a twisted boundary condition. We also show that a testing charge can only be partially screened by conduction electrons, and in strong interaction region the impurity susceptibility has a 1/T-type low temperature behavior.