Parafermion Hall states from coset projections of abelian conformal theories

TL;DR

This paper explores the construction of Z_k-parafermion Hall states from abelian conformal theories, providing new insights into their structure, excitations, and wave functions through coset projections and lattice models.

Contribution

It introduces two abelian parent states that reduce to parafermion states via projection, offering a detailed conformal field theory framework for understanding their excitations.

Findings

Derived simple quasi-particle wave functions for parafermion states.

Provided a complete account of excitations, including field identifications and symmetries.

Established a conformal theory approach using coset construction for parafermion states.

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.