Friedel oscillations for interacting fermions in one dimension

TL;DR

This paper investigates how Friedel oscillations in one-dimensional interacting fermion systems decay with distance, revealing interaction-dependent decay laws and crossover behaviors for different impurity strengths.

Contribution

It provides a comprehensive analysis of Friedel oscillations in 1D electron liquids with arbitrary interactions and impurity strengths, including crossover phenomena.

Findings

Friedel oscillations decay as x^-g in Luttinger liquids.

Weak scatterers exhibit a slower decay at intermediate distances.

Crossover from intermediate decay to asymptotic decay is characterized.

Abstract

We study Friedel oscillations in one-dimensional electron liquid for arbitrary electron-electron interaction and arbitrary impurity strength. For Luttinger liquid leads, the Friedel oscillations decay as x^-g far away from the impurity, where g is the interaction constant. For a weak scatterer, a slower decay is found at intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.