Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9207019

Duality in Multi-layered Quantum Hall Systems

Ting, C.

Published Jul 17, 1992• 0 citations
arXivHTMLPDF

Abstract

The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of the multi-layered FQHE. A many-quasi-hole wavefunction is proposed for the bilayered samples. We also predict a $ν= 5/7$ FQHE for triple-layered samples. The viability of {\em 3-dimensional} FQHE and the application of the concept of generalized duality to anyonic superconductivity are discussed.

DOI
10.48550/arxiv.cond-mat/9207019

Related papers

Duality and anyonic excitations

Wellington da Cruz

We consider anyonic excitations classified into equivalence classes labeled by Hausdorff dimension, $h$ and introduce the concept of duality between such classes, defined by $\tilde{h}=3-h$. In this way, we confirm that the filling factors for which the Fractional Quantum Hall Effect (FQHE) were observed just appears into these classes and the duality in case is between quasihole and quaasiparticle excitations for these FQHE systems.Exchanges of dual pairs $(ν,\tildeν)$, suggests conformal invariance.

arXiv:cond-mat/9802290•Feb 26, 1998•0 citations

Hierarchical wave functions and fractional statistics in fractional quantum Hall effect on the torus

Dingping Li

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis

•Jan 1, 1993•9 citations

Spinning Braid Group Representation and the Fractional Quantum Hall Effect

Ting, C, Lai, C H

The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of {\\em charged} winding number in the super-plane, we represent the braid group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the Hamiltonian, suggesting the possibility of {\\em spinning nonabelian} anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excitations is given. We obtain Laughlin, Halperin and Moore-Read states as {\\em exact} ground state solutions to the respective Hamiltonians associated to the braid group representations. The energy gap of the quasi-excitation is also obtainable from this approach.

•Jan 1, 1993•2 citations

HIERARCHICAL WAVE FUNCTIONS AND FRACTIONAL STATISTICS IN FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

DINGPING LI

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clearly reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.

arXiv:cond-mat/9212033•International Journal of Modern Physics B•Jul 10, 1993•9 citations

COLLECTIVE FIELD THEORY APPLIED TO THE FRACTIONAL QUANTUM HALL EFFECT

BUNJI SAKITA, Dong-Ning Sheng, Zhao-Bin Su

We present an application of collective field theory to the fractional quantum Hall effect (FQHE). We first express the condition, that the electrons are all in the lowest Landau level, as a constraint equation for the state functional. We then derive the fractional filling factor from this equation together with the no-free-vortex assumption. A hierarchy of filling factors is derived by using the particle-vortex dual transformations. In the final section we discuss an attempt at a dynamical theory of FQHE, which would justify the no-free-vortex assumption. A derivation of Laughlin’s wave function with and without quasi-hole excitations is also given.

International Journal of Modern Physics B•Jan 1, 1991•0 citations

Non-Abelian fusion and braiding in many-body parton states

Koyena Bose

Fractional quantum Hall (FQH) states host fractionally charged anyons with exotic exchange statistics. Of particular interest are FQH phases supporting non-Abelian anyons, which can encode topologically protected quantum information. In this work, we construct quasihole bases for a broad family of non-Abelian FQH states using parton wave functions, which reproduces the fusion-space dimensionality expected from their underlying conformal field theory, consistent with level-rank duality across the parton family. As an application, we numerically compute braiding matrices for representative parton states for large systems, providing a general framework for diagnosing non-Abelian characteristics in candidate FQH states.

arXiv:2601.16819•Jan 23, 2026•0 citations
The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of the multi-layered FQHE. A many-quasi-hole wavefunction is proposed for the bilayered samples. We also predict a ν=5/7ν= 5/7ν=5/7 FQHE for triple-layered samples. The viability of {\em 3-dimensional} FQHE and the application of the concept of generalized duality to anyonic superconductivity are discussed.
We consider anyonic excitations classified into equivalence classes labeled by Hausdorff dimension, hhh and introduce the concept of duality between such classes, defined by h~=3−h\tilde{h}=3-hh~=3−h. In this way, we confirm that the filling factors for which the Fractional Quantum Hall Effect (FQHE) were observed just appears into these classes and the duality in case is between quasihole and quaasiparticle excitations for these FQHE systems.Exchanges of dual pairs (ν,ν~)(ν,\tildeν)(ν,ν~), suggests conformal invariance.
The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of {\\em charged} winding number in the super-plane, we represent the braid group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the Hamiltonian, suggesting the possibility of {\\em spinning nonabelian} anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excitations is given. We obtain Laughlin, Halperin and Moore-Read states as {\\em exact} ground state solutions to the respective Hamiltonians associated to the braid group representations. The energy gap of the quasi-excitation is also obtainable from this approach.
We present an application of collective field theory to the fractional quantum Hall effect (FQHE). We first express the condition, that the electrons are all in the lowest Landau level, as a constraint equation for the state functional. We then derive the fractional filling factor from this equation together with the no-free-vortex assumption. A hierarchy of filling factors is derived by using the particle-vortex dual transformations. In the final section we discuss an attempt at a dynamical theory of FQHE, which would justify the no-free-vortex assumption. A derivation of Laughlin’s wave function with and without quasi-hole excitations is also given.
Fractional quantum Hall (FQH) states host fractionally charged anyons with exotic exchange statistics. Of particular interest are FQH phases supporting non-Abelian anyons, which can encode topologically protected quantum information. In this work, we construct quasihole bases for a broad family of non-Abelian FQH states using parton wave functions, which reproduces the fusion-space dimensionality expected from their underlying conformal field theory, consistent with level-rank duality across the parton family. As an application, we numerically compute braiding matrices for representative parton states for large systems, providing a general framework for diagnosing non-Abelian characteristics in candidate FQH states.