Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid. II. Correlation functions

TL;DR

This paper explores how a 2D quantum Hall system confined to a narrow channel can be mapped to a 1D Luttinger liquid, analyzing correlation functions and the effects of interactions on their asymptotic behavior.

Contribution

It derives the low-energy 2D electron correlation function from the 1D Luttinger liquid model, extending previous microscopic mapping studies.

Findings

Correlation functions decay similarly in 2D and 1D systems.

Interactions modify the asymptotic behavior of correlation functions.

The low-energy 2D correlation function reflects the Luttinger liquid characteristics.

Abstract

We study a simple model of a quantum Hall system with the electrons confined to a linear, narrow channel. The system is mapped to a 1D system which in the low-energy approximation has the form of a Luttinger liquid with different interactions between particles of equal and of opposite chiralities. In a previous paper (Part I) we studied this mapping at the microscopic level, and discussed the relation between the parameters of the 2D system and the corresponding 1D Luttinger liquid parameters. We follow up this study here and derive the low-energy form of the 2D electron correlation function by applying the mapping from the 1D correlation function. We examine in particular the modification of the asymptotic behaviour of the correlation function due to interactions and find for the 2D function a similar fall off with distance as in 1D.