The Edge State Network Model and the Global Phase Diagram

2001/04/19 by Kentaro Nomura, Daijiro Yoshioka
Engineering · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Condensed matter physics #Electron #Fractional quantum Hall effect #Mathematics #Phase (matter) #Phase diagram #Phase transition #Physics #Plateau (mathematics) #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum phase transition #Quantum spin Hall effect #Quantum tunnelling #Randomness #Statistical physics #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1143/jpsj.70.2652

5 page RevTex

arxiv created 2001/04/19 · openalex publication_date 2001/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The effects of randomness are investigated in the fractional quantum Hall systems. Based on the Chern-Simons Ginzburg-Landou theory and considering relevant quasi-particle tunneling, the edge state network model for the hierarchical state is introduced and the plateau-plateau transition and liquid-insulator transition are discussed. This model has duality which corresponds to the relation of the quantum Hall liquid phase and the Hall insulating phase and reveals a mechanism in the weak coupling regime.

Citations

• Effective theories of the fractional quantum Hall effect: Hierarchy construction
• Classification of Abelian quantum Hall states and matrix formulation of topological fluids
• Network of Edge States: A Random Josephson Junction Array Description
• Effective theories of the fractional quantum Hall effect at generic filling fractions
• THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS
• Weak Field Phase Diagram for an Integer Quantum Hall Liquid
• Gapless boundary excitations in the quantum Hall states and in the chiral spin states
• Percolation, quantum tunnelling and the integer Hall effect