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arXiv · hep-th/0009229

Parafermion Hall states from coset projections of abelian conformal theories

Andrea Cappelli·Lachezar S. Georgiev·Ivan T. Todorov
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Abstract

The Z_k-parafermion Hall state is an incompressible fluid of k-electron clusters generalizing the Pfaffian state of paired electrons. Extending our earlier analysis of the Pfaffian, we introduce two ``parent'' abelian Hall states which reduce to the parafermion state by projecting out some neutral degrees of freedom. The first abelian state is a generalized (331) state which describes clustering of k distinguishable electrons and reproduces the parafermion state upon symmetrization over the electron coordinates. This description yields simple expressions for the quasi-particle wave functions of the parafermion state. The second abelian state is realized by a conformal theory with a (2k-1)-dimensional chiral charge lattice and it reduces to the Z_k-parafermion state via the coset construction su(k)_1+su(k)_1/su(k)_2. The detailed study of this construction provides us a complete account of the excitations of the parafermion Hall state, including the field identifications, the Z_k symmetry and the partition function.

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Andrea Cappelli, Lachezar S. Georgiev, Ivan T. Todorov. 2000-09-28. Parafermion Hall states from coset projections of abelian conformal theories. https://doi.org/10.1016/s0550-3213(00)00774-4

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