Dissipation-driven quantum phase transitions in a Tomonaga-Luttinger liquid electrostatically coupled to a metallic gate

TL;DR

This paper investigates how a metallic gate causes dissipation in a 1D electron liquid, leading to quantum phase transitions from a Tomonaga-Luttinger liquid to dissipative phases, with implications for low-energy electronic properties.

Contribution

It introduces a model for dissipation effects on 1D electron liquids and identifies quantum phase transitions induced by a metallic gate, including a dual model with Josephson coupling.

Findings

Quantum phase transition from Tomonaga-Luttinger liquid to dissipative phases.

Identification of a phase with finite spatial correlation length.

Dual model describing an attractive 1D metal with Josephson coupling.

Abstract

The dissipation induced by a metallic gate on the low-energy properties of interacting 1D electron liquids is studied. As function of the distance to the gate, or the electron density in the wire, the system undergoes a quantum phase transition from the Tomonaga-Luttinger liquid state to two kinds of dissipative phases, one of them with a finite spatial correlation length. We also define a dual model, which describes an attractive one dimensional metal with a Josephson coupling to a dirty metallic lead.