Bridge Between Abelian and Non-Abelian Fractional Quantum Hall States

2008/04/30 by Nicolas Regnault, N. Regnault, M. O. Goerbig +2 · 1 citation
Engineering · Materials Science · Mathematics · Medicine · Physics and Astronomy · #Abelian group #Advancements in Semiconductor Devices and Circuit Design #Bridge (graph theory) #Composite fermion #Condensed matter physics #Electron #Fractional quantum Hall effect #Graphene research and applications #Mathematical physics #Mathematics #Medicine #Physics #Pure mathematics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.101.066803

published as Phys. Rev. Lett. 101, 066803 (2008) · 4 pages, 2 figures; revised version, published in Phys. Rev. Lett

openalex publication_date 2008/08/06 · arxiv created 2008/08/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that K-component Halperin wave functions may be a common basis for both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

Citations

• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory
• Nonabelions in the fractional quantum hall effect

Cited by

• Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase