Metal-Insulator Transition of the Quasi-One Dimensional Luttinger Liquid Due to the Long-Range Character of the Coulomb Interaction

TL;DR

This paper investigates how long-range Coulomb interactions induce a metal-insulator transition in quasi-one-dimensional Luttinger liquids, leading to charge-density wave formation and a dielectric gap at the Fermi surface.

Contribution

It demonstrates the instability of the homogeneous metallic state and calculates the dielectric gap resulting from long-range Coulomb interactions in quasi-1D systems.

Findings

Homogeneous metal ground state is unstable

Charge-density wave forms with specific wavevector components

Dielectric gap at the Fermi surface is quantitatively calculated

Abstract

An instability of the quasi-1D Luttinger liquid associated with the metal - insulator transition is considered. The homogeneous metal ground state of this liquid is demonstrated to be unstable and the charge-density wave arises in the system. The wavevector of this wave has nonzero component both along the direction of the chains and in the perpendicular direction. The ground state of the system has a dielectric gap at the Fermi surface, the value of this gap being calculated.