Comment on "Strongly correlated Fractional Quantum Hall line junction"

TL;DR

This paper critiques a previous exact solution for a fractional quantum Hall line junction, providing a corrected solution for a specific case to clarify the theoretical understanding of such systems.

Contribution

It identifies errors in prior solutions and offers a corrected, accurate solution for a specific instance of the fractional quantum Hall line junction model.

Findings

Previous solutions were incorrect

Provides a correct solution for a specific case

Clarifies theoretical understanding of quantum Hall junctions

Abstract

Physical Review Letter {\bf 90}, 026802 (2003) by U. Z\"{u}licke and E. Shimshoni and subsequent extended paper proposed an ``exact solution'' of the problem of a tunnel junction of length $L$ between two single-mode edges of the Fractional Quantum Hall Liquids with different filling factors $\nu_{j}=1/(2m_j+1)$, $j=1,2$; $m_j=0,1,...$. The purpose of this comment is to point out that the solution found in these papers is not correct and to present correct solution of a particular instance of this model.