# Coulomb interaction driven instabilities of sliding Luttinger liquids

## TL;DR

This paper investigates arrays of coupled quantum wires with Coulomb interactions, revealing a higher-dimensional sliding Luttinger liquid state that is unstable to charge density wave formations under certain conditions.

## Contribution

It introduces a bosonization-based analysis of Coulomb-driven instabilities in coupled quantum wires, identifying various charge density wave states and their ordering patterns.

## Key findings

- Identification of a higher-dimensional sliding Luttinger liquid phase.
- Charge density wave states are favored by weak interwire backscatterings.
- Determination of specific ordering patterns and associated energy scales.

## Abstract

We study systems made of periodic arrays of one dimensional quantum wires, coupled by Coulomb interaction. Using bosonization an interacting metallic fixed point is obtained, which is shown to be a higher dimensional analogue of the Tomonaga-Luttinger liquid, or a sliding Luttinger liquid. This non-Fermi liquid metallic state, however, is unstable in the presence of weak interwire backscatterings, which favor charge density wave states and suppress pairing. Depending on the effective strength of the Coulomb repulsion and the size of interwire spacing various charge density wave states are stabilized, including Wigner crystal states. Our method allows for the determination of the specific ordering patterns, and corresponding energy and temperature scales.