Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases

Abstract

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general quantum Hall states have many edge states. Here we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve in all cases explicit derivative operators diminishing the angular momentum of the system.

12 pages, entirely revised version, major conceptual changes

References in corpus (3)

• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3

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• PH Pfaffian intra and inter correlations in the quantum Hall bilayer
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level