Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states by Barkeshli, Maissam, Wen, Xiao-Gang

“…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). …”
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U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states by Barkeshli, Maissam, Wen, Xiao-Gang

“…These results allow us to show that l=3 U(1)×U(1)⋊Z2 Chern-Simons theory is the low-energy effective theory for the Z4 parafermion (Read-Rezayi) fractional quantum Hall states, which occur at filling fraction ν=2/2k−3. …”
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Structure of quasiparticles and their fusion algebra in fractional quantum Hall states by Barkeshli, Maissam, Wen, Xiao-Gang

“…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.…”
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Classification of Abelian and non-Abelian multilayer fractional quantum Hall states through the pattern of zeros by Barkeshli, Maissam, Wen, Xiao-Gang

“…Such a classification leads to the construction of a class of non-Abelian multilayer FQH states that are closely related to ĝk parafermion conformal field theories, where ĝk [g superscript k] is an affine simple Lie algebra. …”
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Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States by Barkeshli, Maissam, Wen, Xiao-Gang

“…One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z[subscript 4] parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. …”
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Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States by Barkeshli, Maissam, Wen, Xiao-Gang

“…One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. …”
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Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states by Barkeshli, Maissam, Wen, Xiao-Gang

“…We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z[subscript 4] parafermion (Read-Rezayi) state is a special case. This provides an example in which Z[subscript 2] electron fractionalization leads to non-Abelian topological phases. …”
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Topological order in the fractional quantum Hall states by Barkeshli, Maissam

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