Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros

2008/03/31 by Xiao-Gang Wen, Zhenghan Wang · 1 citation
Mathematics · Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el #math-ph #math.MP

paper · pdf · doi:10.1103/physrevb.78.155109

published as Phys. Rev. B 78, 155109 (2008) · 26 pages. RevTeX4

arxiv created 2008/05/03 · openalex publication_date 2008/10/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It has been shown that different Abelian and non-Abelian fractional quantum Hall states can be characterized by patterns of zeros described by sequences of integers S_a. In this paper, we will show how to use the data S_a to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as well as the actions of the quasiparticle tunneling and modular transformations on the degenerate ground states on torus.

Citations

• Chiral Operator Product Algebra Hidden in Certain Fractional Quantum Hall Wave Functions
• Appearance of Gauge Structure in Simple Dynamical Systems
• Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus
• THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS
• String-net condensation: A physical mechanism for topological phases
• Anyons in an exactly solved model and beyond
• Nonabelions in the fractional quantum hall effect

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