Construction of edge states in fractional quantum Hall systems by Jack polynomials

Abstract

We study the edge-mode excitations of a fractional quantum Hall droplet by expressing the edge-state wave functions as linear combinations of Jack polynomials with a negative parameter. We show that the exact diagonalization within a subspace of Jack polynomials can be used to generate the chiral edge-mode excitation spectrum in the Laughlin phase and the Moore-Read phase with realistic Coulomb interaction. The truncation technique for the edge excitations simplifies the procedure to reliably extract the edge-mode velocities, which avoids the otherwise complicated analysis of the full spectrum that contains both edge and bulk excitations. Generalization to the Read-Rezayi state is also discussed.