Fractional quantum Hall states as an Abelian group

2014/03/31 by Alí Nassar, Ali Nassar
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Combinatorics #Electron #Fractional quantum Hall effect #Group (periodic table) #Mathematical physics #Mathematics #Order (exchange) #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Hall effect #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #Topological order #Topology (electrical circuits) #cond-mat.str-el #hep-th

paper · pdf · doi:10.1016/j.physleta.2014.12.033

published as Physics Letters A 379 (2015), pp. 643-645 · 9 pages

openalex publication_date 2014/12/22 · arxiv created 2015/01/30 · arxiv updated 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that the set of double-layer Fractional Quantum Hall (FQH) states with a given topological order form a finite Abelian group under a new product. This group structure makes it possible to construct new FQH states from known ones. We also introduce a new index which can be used to characterize the topological order of FQH states.

Citations

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• TOPOLOGICAL ORDERS IN RIGID STATES
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• THE GROUND STATE STRUCTURE AND MODULAR TRANSFORMATIONS OF FRACTIONAL QUANTUM HALL STATES ON A TORUS