Pattern-of-Zeros Approach to Fractional Quantum Hall States and a Classification of Symmetric Polynomial of Infinite Variables

  • Xiao-Gang Wen
  • Zhenghan Wang
Part of the Mathematical Lectures from Peking University book series (MLPKU)


Some purely chiral fractional quantum Hall states are described by symmetric or anti-symmetric polynomials of infinite variables. In this article, we review a systematic construction and classification of those fractional quantum Hall states and the corresponding polynomials of infinite variables, using the pattern-of-zeros approach. We discuss how to use patterns of zeros to label different fractional quantum Hall states and the corresponding polynomials. We also discuss how to calculate various universal properties (i.e. the quantum topological invariants) from the pattern of zeros.



This research is supported by NSF Grant No. DMR-1005541 and NSFC 11074140.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Xiao-Gang Wen
    • 1
    • 2
  • Zhenghan Wang
    • 3
  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Institute for Advanced StudyTsinghua UniversityBeijingP.R. China
  3. 3.Microsoft Station QUniversity of CaliforniaSanta BarbaraUSA

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