Composite Fermion Wavefunctions Derived by Conformal Field Theory

TL;DR

This paper links Jain hierarchical Hall wavefunctions to conformal field theory, specifically W-infinity minimal models, revealing a connection that explains quasihole excitations with non-Abelian statistics.

Contribution

It demonstrates that Jain wavefunctions can be derived from W-infinity minimal models, providing a conformal field theory framework for hierarchical quantum Hall states.

Findings

Exact relation between Jain wavefunctions and CFT correlators

Identification of W-infinity minimal models as the underlying CFT

Quasihole excitations exhibit non-Abelian fractional statistics

Abstract

The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal theory is precisely given by the W-infinity minimal models introduced earlier. This theory involves a reduction of the multicomponent Abelian theory that is similar to the projection to the lowest Landau level in the Jain approach. The projection yields quasihole excitations obeying non-Abelian fractional statistics. The analysis closely parallels the bosonic conformal theory description of the Pfaffian and Read-Rezayi states.