Instability of sliding Luttinger liquid

TL;DR

This paper revises the phase diagram of the sliding Luttinger liquid in coupled quantum wires, analyzing how realistic inter-wire interactions influence the stability of the phase, and identifying conditions under which it can be stabilized.

Contribution

It provides a detailed analysis of the stability of the SLL phase under physically justifiable inter-wire interactions, highlighting the conditions that can preserve the phase.

Findings

Inter-wire interactions generally destabilize the SLL phase.

Suppressing inter-wire tunneling can lead to a stable SLL region.

Screened Coulomb interactions influence phase stability.

Abstract

We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or "Coulomb-blockade" type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire interaction.