Effects of Long Range Electronic Interactions on a One-dimensional Electron System

TL;DR

This paper investigates how long-range Coulomb interactions influence a one-dimensional spinless fermion system, revealing a quasi-metallic phase distinct from Luttinger liquids and a transition to a localized charge density wave at strong interactions.

Contribution

It combines numerical and analytical methods to show that long-range interactions induce a unique quasi-metallic state and a crossover to charge localization, challenging existing Luttinger liquid models.

Findings

Enhanced metallic character at intermediate scales due to long-range interactions

Identification of a non-Luttinger liquid quasi-metallic regime

Observation of a transition to a charge density wave at high interaction strength

Abstract

The effects of a long range electronic potential on a one dimensional chain of spinless fermions are investigated by numerical techniques (Exact Diagonalisation of rings with up to 30 sites complemented by finite size analysis) and analytic calculations. Due to a competition between the $2 k_F$ oscillations in the density and the (very slow) log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) lengthscales. Despite some similarities, we found that this quasi-metallic regime is not of the Luttinger Liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substancially increased, we observe a smooth cross-over to a strongly localized charge density wave.