Edge Excitations of the $\nu = 2/3$ Spin-Singlet Quantum Hall State

TL;DR

This paper derives the edge excitation spectrum of the spin-unpolarized $ u=2/3$ fractional quantum Hall state, confirming the existence of oppositely directed spin and charge branches and analyzing their algebraic structure and conductance implications.

Contribution

It provides a detailed theoretical and numerical analysis of the edge excitations in the $ u=2/3$ spin-singlet state, revealing the algebraic structure and coupling of spin and charge branches.

Findings

Edge $ u=2/3$ state has oppositely directed spin and charge branches.

Same $SU(2)_{k=1}$ algebra describes all unmixed spin branches.

Less coupling between spin and charge branches suggests conductance changes at transitions.

Abstract

The spectrum of edge excitations is derived for the spin-unpolarized $\nu = 2$ and $\nu = 2/3$ FQHE. Numerical diagonalization of a system of six electrons on a disc confirms that the edge $\nu = 2/3$ spin-singlet FQHE state consists of oppositely directed spin and charge branches on the same physical edge. The highly correlated $\nu = 2/3$ singlet edge is shown to have the same spin branch as the $\nu = 2$ singlet edge, providing evidence that the same $SU(2)_{k = 1}$ Kac-Moody algebra describes all unmixed spin branches. The spin and charge branches of the singlet state at $\nu = 2/3$ are less coupled than the two branches of the spin-polarized state at the same filling factor, suggesting that the conductance along an edge may increase sharply across the polarized-unpolarized transition.