Electron operator at the edge of the 1/3 fractional quantum Hall liquid

Abstract

This study builds upon the work of Palacios and MacDonald (Phys. Rev. Lett. {\bf 76}, 118 (1996)), wherein they identify the bosonic excitations of Wen's approach for the edge of the 1/3 fractional quantum Hall state with certain operators introduced by Stone. Using a quantum Monte Carlo method, we extend to larger systems containing up to 40 electrons and obtain more accurate thermodynamic limits for various matrix elements for a short range interaction. The results are in agreement with those of Palacios and MacDonald for small systems, but offer further insight into the detailed approach to the thermodynamic limit. For the short range interaction, the results are consistent with the chiral Luttinger liquid predictions.We also study excitations using the Coulomb ground state for up to nine electrons to ascertain the effect of interactions on the results; in this case our tests of the chiral Luttinger liquid approach are inconclusive.

arXiv comment10 pages, 2 figures

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Cited by in corpus (8)

• Testing the topological nature of the fractional quantum Hall edge
• 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
• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• Universality Lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect