Fractional-quantum-Hall edge electrons and Fermi statistics

TL;DR

This paper investigates whether electrons at fractional quantum Hall edges obey Fermi statistics, providing numerical evidence that they generally do not, challenging common assumptions and impacting interpretations of tunneling experiments.

Contribution

The study demonstrates through numerical calculations that electrons at fractional quantum Hall edges do not necessarily follow Fermi statistics, questioning existing theoretical models.

Findings

Electrons at fractional quantum Hall edges may violate Fermi statistics.

Numerical evidence shows standard bosonization expressions are inconsistent with finite-size data.

Experimental tunneling results should be reinterpreted in light of non-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.