Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states
Author(s)Barkeshli, Maissam; Wen, Xiao-Gang
Effective field theory and projective construction for Zk parafermion fractional quantum Hall states
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The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the simpler integer quantum Hall states. Here we show how to apply the projective construction to the Z[subscript k] parafermion (Laughlin/Moore-Read/Read-Rezayi) FQH states, which occur at filling fraction ν=k/(kM+2). This allows us to derive the bulk low-energy effective field theory for these topological phases, which is found to be a Chern-Simons theory at level 1 with a U(M)×Sp(2k) gauge field. This approach also helps us understand the non-Abelian quasiholes in terms of holes of the integer quantum Hall states.
DepartmentMassachusetts Institute of Technology. Department of Physics
Physical Review B
American Physical Society
Barkeshli, Maissam, and Xiao-Gang Wen. “Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states.” Physical Review B 81.15 (2010): 155302. © 2010 The American Physical Society.
Final published version