Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States

TL;DR

This paper applies the projective construction to Z_k parafermion fractional quantum Hall states, deriving their effective field theories and elucidating the nature of non-Abelian quasiholes.

Contribution

It extends the projective construction method to Z_k parafermion FQH states, deriving their bulk effective field theory as a Chern-Simons theory with specific gauge fields.

Findings

Derived the bulk low energy effective field theory as a Chern-Simons theory.

Provided a framework to understand non-Abelian quasiholes via integer quantum Hall holes.

Connected the projective construction to topological phases at filling fraction  = k/(kM+2).

Abstract

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_k parafermion (Laughlin/Moore-Read/Read-Rezayi) FQH states, which occur at filling fraction \nu = 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) \times Sp(2k) gauge field. This approach also helps us understand the non-Abelian quasiholes in terms of holes of the integer quantum Hall states.