Numerical tests of Fermi statistics on fractional quantum Hall edges

和住 猪野

Ulrich Zülicke, Juan Jose Palacios, Allan H. MacDonald

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 $\ensuremath{\nu}=2/5$ 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.

B. G. Wybourne

Shivakumar Jolad, Jainendra K. Jain

We carry out numerical diagonalization for much larger systems than before by restricting the fractional quantum Hall (FQH) edge excitations to a basis that is exact for a short-range interaction and very accurate for the Coulomb interaction. This enables us to perform substantial tests of the predicted universality of the edge physics. Our results suggest the possibility that the behavior of the FQH edge is intrinsically nonuniversal, even in the absence of edge reconstruction, and therefore may not bear a sharp and unique relation to the nature of the bulk FQH state.

D. Yoshioka

Juan Jose Palacios, Allan H. MacDonald

We report on microscopic numerical studies that support the chiral Luttinger liquid theory of the fractional Hall edge proposed by Wen. Our calculations are based in part on newly proposed and accurate many-body trial wave functions for the low-energy edge excitations of fractional incompressible states.