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.

arXiv comment9 pages, 1 figure, RevTex4

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• Edge excitations and Topological orders in rotating Bose gases
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling
• Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge
• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Electron operator at the edge of the 1/3 fractional quantum Hall liquid
• Microscopic study of the 2/5 fractional quantum Hall edge
• Transport of fractional Hall quasiparticles through an antidot
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Temperature dependent equilibration of spin orthogonal quantum Hall edge modes
• The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems
• Fractional Quantum Hall Edge Electrons, Chiral Anomaly and the Berry Phase
• Universality Lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect