Renormalization group study of Luttinger liquids with boundaries

TL;DR

This paper applies Wilson's renormalization group method to analyze one-dimensional Luttinger liquids with open boundaries, demonstrating that certain interaction terms are irrelevant and reinforcing the theoretical foundation for these systems.

Contribution

It provides a rigorous RG analysis showing the irrelevance of commonly neglected interaction terms in Luttinger liquids with boundaries, strengthening the theoretical basis.

Findings

Neglected two-particle interactions are RG-irrelevant.

Supports the validity of bosonization in boundary systems.

Enhances understanding of boundary effects in Luttinger liquids.

Abstract

We use Wilsons weak coupling ``momentum'' shell renormalization group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed irrelevant in the renormalization group sense. Our study provides a more solid ground for many investigations of Luttinger liquids with open boundaries.