Form-factors computation of Friedel oscillations in Luttinger liquids

TL;DR

This paper presents an analytical method to compute Friedel oscillations in the charge density of a one-dimensional Luttinger liquid with a single impurity for interaction parameter g less than or equal to 1/2.

Contribution

It introduces a novel analytical approach for calculating Friedel oscillations in Luttinger liquids with strong interactions (g ≤ 1/2).

Findings

Analytical expressions for Friedel oscillations derived.

Applicable for g ≤ 1/2 in Luttinger liquids.

Enhances understanding of impurity effects in 1D systems.

Abstract

We show how to analytically determine for $g\leq 1/2$ the "Friedel oscillations" of charge density by a single impurity in a 1D Luttinger liquid of spinless electrons.