Non-Abelian quantum Hall states and their quasiparticles: From the pattern of zeros to vertex algebra
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Lu-2010-Non-Abelian quantum.pdf
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Author(s)
Lu, Yuan-Ming
Wen, Xiao-Gang
Wang, Zhenghan
Wang, Ziqiang
Date Issued
March 2010
Journal
Physical Review B
Publisher
American Physical Society
Citation
Lu, Yuan-Ming et al. “Non-Abelian quantum Hall states and their quasiparticles: From the pattern of zeros to vertex algebra.” Physical Review B 81.11 (2010): 115124. © 2010 The American Physical Society.
Version
Final published version
Abstract
In the pattern-of-zeros approach to quantum Hall states, a set of data {n;m;S[subscript a]|a=1,…,n;n,m,S[subscript a]∊N} (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data {n;m;S[subscript a]} corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the pattern of zeros alone does not completely characterize the quantum Hall states. In this paper, we find that the following expanded set of data {n;m;S[subscript a];c|a=1,…,n;n,m,S[subscript a]∊N;c∊R} provides a more complete characterization of quantum Hall states. Each expanded set of data completely characterizes a unique quantum Hall state, at least for the examples discussed in this paper. The result is obtained by combining the pattern of zeros and Zn simple-current vertex algebra which describes a large class of Abelian and non-Abelian quantum Hall states [phi]Zn[superscript sc]. The more complete characterization in terms of {n;m;S[subscript a];c} allows us to obtain more topological properties of those states, which include the central charge c of edge states, the scaling dimensions and the statistics of quasiparticle excitations.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.81.115124
