Topological orders and edge excitations in fractional quantum Hall states

1995/06/30 by Xiao-Gang Wen · 3 citations
Mathematics · Physics and Astronomy · #Characterization (materials science) #Computer science #Condensed matter physics #Electron #Enhanced Data Rates for GSM Evolution #Fractional quantum Hall effect #Mathematics #Measure (data warehouse) #Optics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat

paper · pdf · doi:10.1080/00018739500101566

published as Advances in Physics, 44, 405 (1995) · 67 pages, plain-tex, 3 figures. The section about spin vector was rewritten to make it more readable

openalex publication_date 1995/10/01 · arxiv created 1995/10/31 · arxiv updated 2009/11/30 · openalex created_date 2020/08/10 · openalex updated_date 2026/08/08

Abstract

Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss the characterization and classification of the new orders (which are called topological orders). We also discuss the edge excitations in FQH liquids, which form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at the edges also have very rich structures as a reflection of the rich topological orders in the bulk. Thus edge excitations provide us a practical way to measure topological orders in experiments.

Citations

• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Orbital spins of the collective excitations in Hall liquids
• Chiral Operator Product Algebra Hidden in Certain Fractional Quantum Hall Wave Functions
• Excitation structure of the hierarchy scheme in the fractional quantum Hall effect
• Current algebra and Wess-Zumino model in two dimensions
• Two-Dimensional Magnetotransport in the Extreme Quantum Limit
• Quantum field theory and the Jones polynomial
• TOPOLOGICAL ORDERS AND CHERN-SIMONS THEORY IN STRONGLY CORRELATED QUANTUM LIQUID
• Remarks on the canonical quantization of the Chern-Simons-Witten theory
• Equivalence of the resonating-valence-bond and fractional quantum Hall states
• Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
• Classification of Abelian quantum Hall states and matrix formulation of topological fluids
• Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems
• Effective theories of the fractional quantum Hall effect at generic filling fractions
• THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS
• Sharp and smooth boundaries of quantum Hall liquids
• Gapless boundary excitations in the quantum Hall states and in the chiral spin states
• Nonabelions in the fractional quantum hall effect

Cited by

• Gapped Boundaries of Kitaev's Quantum Double Models: A Lattice Realization of Anyon Condensation from Lagrangian Algebras
• Hamiltonian quantization of complex Chern-Simons theory at level-k
• Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality