Unscreened Coulomb repulsion in the one dimensional electron gas

TL;DR

This paper investigates a one-dimensional electron gas with unscreened Coulomb interactions using DMRG, revealing Wigner crystal formation and showing that long-range forces suppress Umklapp scattering at finite doping.

Contribution

It demonstrates the applicability of DMRG to long-range Coulomb interactions and provides a detailed analysis of correlation functions supporting Wigner crystal formation.

Findings

Wigner crystal formation confirmed in 1D electron gas

Long-range Coulomb forces suppress Umklapp scattering at finite doping

DMRG effectively applied to long-range interaction models

Abstract

A tight binding model of electrons interacting via bare Coulomb repulsion is numerically investigated by use of the Density Matrix Renormalization Group method which we prove applicable also to very long range potentials. From the analysis of the elementary excitations, of the spin and charge correlation functions and of the momentum distribution, a picture consistent with the formation of a one dimensional "Wigner crystal" emerges, in quantitative agreement with a previous bosonization study. At finite doping, Umklapp scattering is shown to be ineffective in the presence of long range forces.