A Luttinger Liquid coupled to Ohmic-class environments

TL;DR

This paper studies how Ohmic-class environments influence the conduction, correlations, and phase transitions in one-dimensional Luttinger liquids, revealing environment-induced engineering of interactions and modifications to the metal-insulator transition.

Contribution

It demonstrates that Ohmic environments preserve the Kane-Fisher transition, while sub- and super-Ohmic environments alter it into a crossover, considering realistic experimental conditions.

Findings

Ohmic environments preserve the metal-insulator transition.

Sub- and super-Ohmic environments modify the transition into a crossover.

Finite length and temperature affect transport properties.

Abstract

We investigate the impact of an Ohmic-class environment on the conduction and correlation properties of one-dimensional interacting systems. Interestingly, we reveal that inter-particle interactions can be engineered by the environment's noise statistics. Introducing a backscattering impurity to the system, we address Kane-Fisher's metal-to-insulator quantum phase transition in this noisy and realistic setting. Within a perturbative renormalization group approach, we show that the Ohmic environments keep the phase transition intact, while sub- and super-Ohmic environments, modify it into a smooth crossover at a scale that depends on the interaction strength within the wire. The system still undergoes a metal-to-insulator-like transition when moving from sub-Ohmic to super-Ohmic environment noise. We cover a broad range of realistic experimental conditions, by exploring the impact of a finite wire length and temperature on transport through the system.