Tomonaga-Luttinger Liquid Renormalized by a Single Impurity

TL;DR

This paper develops a boundary bosonization method to analyze how a single impurity affects the properties of a spinful Tomonaga-Luttinger liquid, revealing renormalization of parameters due to impurity transmission.

Contribution

A new bosonization formula that smoothly interpolates between strong and weak impurity limits, enabling analysis of impurity effects on TL liquid properties.

Findings

TL parameters are renormalized by impurity-induced partial transmission

The formula connects existing strong and weak impurity theories

Impurity potential modifies bulk correlation functions

Abstract

Effects of a single impurity potential on bulk properties of a spinful Tomonaga-Luttinger (TL) liquid is studied. A boundary bosonization technique is developed to include the impurity potential of {\it arbitrary} strength $V$. Our new bosonization formula for fermion field $\psi$ smoothly connects the two existing expressions in the strong ($V = \infty$) and the weak ($V = 0$) impurity limits. With use of the formula, we found the TL parameters determined from the long-distance correlation functions are renormalized due to the partial transmission through the impurity potential.