Friedel oscillations in one-dimensional metals: from Luttinger's theorem to the Luttinger liquid

TL;DR

This paper studies Friedel oscillations in one-dimensional metals using exact and approximate many-body methods, revealing how local approximations capture different oscillation components depending on system magnetization.

Contribution

It compares exact and approximate methods to analyze Friedel oscillations, highlighting the effects of magnetization and self-interaction corrections in local density approximations.

Findings

Local approximations reproduce different Fourier components based on magnetization.

Self-interaction correction influences the accuracy of local density approximations.

Numerical and analytical methods complement each other in understanding Friedel oscillations.

Abstract

Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe-Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations.