Anyons, boundary constraint, and hierarchy in fractional quantum hall effect

Abstract

Calculations on finite-size systems are carried out to examine the hierarchy theory of the fractional quantum Hall effect. The concept of quasiparticle and quasihole is justified to remain valid at high densities. Numerical results reveal a hard-core boundary constraint on the anyonic quasiparticles so that their wave function must vanish as two of them get close in space. The dynamics of this constraint originates from a strong short-range repulsion between the quasiparticles. The observed quasiparticle-quasihole asymmetry in the hierarchy is understood through the hard-core anyon theory.