A Novel CFT Approach to Bulk Wave Functions in the Fractional Quantum Hall Effect

TL;DR

This paper introduces a conformal field theory approach using non-unitary b/c-spin systems to model bulk wave functions in the fractional quantum Hall effect, providing new insights into fractional statistics and filling fractions.

Contribution

It presents a novel CFT framework for fractional quantum Hall states, extending Jain's series and linking to multilayer K-matrix classifications.

Findings

Derives CFT proposals for various filling fractions.

Provides a geometric interpretation involving ramified coverings.

Classifies experimentally observed filling fractions without unobserved ones.

Abstract

We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of non-unitary b/c-spin systems. These yield a promising conformal field theory analogon of the composite fermion picture of Jain. Fractional statistics is described by twist fields which naturally appear in the b/c-spin systems. We provide a geometrical interpretation of our approach in which bulk wave functions are seen as holomorphic functions over a ramified covering of the complex plane, where the ramification precisely resembles the fractional statistics of the quasi-particle excitations in terms of branch points on the complex plane. To extend Jain's main series, we use the concept of composite fermions pairing to spin singlets, which enjoys a natural description in terms of the particular c=-2 b/c-spin system as known from the Haldane-Rezayi state. In this way we derive conformal field theory proposals for lowest Landau level bulk wave functions for more general filling fractions. We obtain a natural classification of the experimentally confirmed filling fractions which does not contain prominent unobserved fillings. Furthermore, our scheme fits together with classifications in terms of K-matrices of effective multilayer theories leading to striking restrictions of these coupling matrices.