Capacitance and Transport through an Isolated Impurity Center in 1D Luttinger Liquid

TL;DR

This paper explores the relationship between a potential scatterer in a 1D Luttinger liquid and an anisotropic Kondo model, deriving exact formulas for capacitance and conductance using Bethe ansatz.

Contribution

It establishes a theoretical equivalence between impurity scattering in Luttinger liquids and Kondo models, providing non-perturbative analytical results.

Findings

Derived exact expressions for capacitance and conductance.

Established equivalence between impurity scattering and Kondo models.

Used Bethe ansatz for non-perturbative analysis.

Abstract

We establish the equivalence between the problem of a solitary potential scatterer in a Luttinger liquid of spinless repulsive fermions and an anisotropic Kondo model where the value of the impurity spin id determined by the scaling dimension of the scattering potential. The Bethe ansatz is used to derive non-perturbative expressions for the capacitance and conductance.