Fractional-quantum-Hall edge electrons and Fermi statistics

Abstract

We address the quantum statistics of electrons created in the low-energy edge-state Hilbert space sector of incompressible fractional quantum Hall states, considering the possibility that they may not satisfy Fermi statistics. We argue that this property is not a priori obvious, and present numerical evidence based on finite-size exact-diagonalization calculations that it does not hold in general. We discuss different possible forms for the expression for the electron creation operator in terms of edge boson fields and show that none are consistent with our numerical results on finite-size filling-factor-2/5 states with short-range electron-electron interactions. Finally, we discuss the current body of experimental results on tunneling into quantum Hall edges in the context of this result.