Structure of quasiparticles and their fusion algebra in fractional quantum Hall states
Name
Barkeshli-2009-Structure of quasipa.pdf
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Author(s)
Barkeshli, Maissam
Wen, Xiao-Gang
Date Issued
May 2009
Journal
Physical Review B
Publisher
American Physical Society
Citation
Barkeshli, Maissam , and Xiao-Gang Wen. “Structure of quasiparticles and their fusion algebra in fractional quantum Hall states.” Physical Review B 79.19 (2009): 195132. © 2009 The American Physical Society
Version
Final published version
Abstract
It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevB.79.195132
