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

Abstract

The spectrum of edge excitations is derived for the spin-unpolarized $ν= 2$ and $ν= 2/3$ FQHE. Numerical diagonalization of a system of six electrons on a disc confirms that the edge $ν= 2/3$ spin-singlet FQHE state consists of oppositely directed spin and charge branches on the same physical edge. The highly correlated $ν= 2/3$ singlet edge is shown to have the same spin branch as the $ν= 2$ 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 $ν= 2/3$ 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.