Formation of an edge striped phase in the $\nu =\frac{1}{3}$ fractional quantum Hall system

We have performed an exact diagonalization study of up to $N=12\mathrm{}$ interacting electrons on a disk at filling $\nu =\frac{1}{3}$ for both true Coulomb interaction, and the $V_1$ Haldane short-range interaction for which Laughlin wave function is the exact solution. For the Coulomb interaction and $N>~10$ we find persistent radial oscillations in electron density, which are not captured by the Laughlin wave function. Our results strongly suggest formation of a chiral striped phase at the edge of the fractional quantum Hall systems. The amplitude of the charge density oscillations decays slowly, only as a power law with the distance from the edge. Thus the spectrum of edge excitations is likely to be affected.