Edge states of integral quantum Hall states versus edge states of antiferromagnetic quantum spin chains

TL;DR

This paper establishes a correspondence between edge states in integral quantum Hall systems and those in SU(2N) antiferromagnetic quantum spin chains, providing insights into localization phenomena and surface states.

Contribution

It introduces a novel network model approach linking quantum Hall edge states to SU(2N) spin chains, offering qualitative explanations for recent experimental results.

Findings

Edge states of quantum Hall liquids relate to SU(2N) antiferromagnetic spin chains.

Absence of localization explained by gapless excitations in SU(2N) ferromagnetic chains.

Comparison of edge state structures enhances understanding of two-dimensional electron systems.

Abstract

Using the network model representation, it is shown that the edge states of finite-size integral quantum Hall liquid can be regarded as the edge states of an SU$(2N)$ open antiferromagnetic quantum spin chain in the $N \rightarrow 0$ limit. The structures of edge states in both cases of integer quantum Hall liquid and an SU$(2N)$ antiferromagnetic quantum spin chain are compared and the relations between them are pointed out. This correspondence is used to give qualitative arguments in favor of the recent results on two-dimensional electron systems coupled in layers with a large perpendicular magnetic field. In particular, it is shown that the absence of the localization in the two-dimensional chiral surface state of the integral quantum Hall liquid in the case of the finite-size coupled system can be explained by the absence of the gap in the excitation spectrum of an SU$(2N)$ ferromagnetic quantum spin chain in the $N \rightarrow 0$ limit.