2014/03/31 by Abolhassan Vaezi, Maissam Barkeshli · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Anyon #Charge (physics) #Condensed matter physics #Fibonacci number #Graphene research and applications #Magnetic field #Mathematics #Physics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological quantum computer #Torus #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.113.236804
published as Phys. Rev. Lett. 113, 236804 (2014) · 5+9 pages. Accepted for publication in Phys. Rev. Lett
arxiv created 2014/11/06 · openalex publication_date 2014/12/03 · arxiv updated 2014/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.