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

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.

7 pages, LaTeX using prb.sty, 2 short PostScript figures

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