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Classification of Abelian quantum Hall states and matrix formulation of topological fluids

1992/07/15 by Xiao-Gang Wen, A. Zee · 10 citations
Physics and Astronomy · Materials Science · Mathematics · #Quantum and electron transport phenomena #Physics of Superconductivity and Magnetism #Graphene research and applications #Quantum Hall effect #Physics #Topological order #Quantum mechanics #Topology (electrical circuits) #Matrix (chemical analysis) #Fractional quantum Hall effect #Simple (philosophy) #Basis (linear algebra) #Abelian group #Theoretical physics #Quantum #Quantum spin Hall effect #Pure mathematics #Mathematics #Electron #Combinatorics #Geometry

paper · doi:10.1103/physrevb.46.2290

openalex publication_date 1992/07/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/14

Abstract

We give a simple and unified treatment of quantum topological fluids such as the quantum Hall fluid. We show that the order in such fluids can be characterized by a symmetric matrix K, in terms of which various physical quantities can be determined. We construct K by a matrix iteration procedure which may be decomposed into two simple elementary steps. The hierarchy construction is shown to be contained in our matrix iteration construction. The relationship between the vortex basis and the dual electron basis is clarified. We also show that under certain mild assumptions the generalized hierarchy construction exhausts all possible Abelian fractional quantum Hall states. We identify and determine the topological quantity known as the shift. Our formalism may be relevant for recent experimental data on multilayered systems.

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