Conformal Field Theory of Composite Fermions

TL;DR

This paper demonstrates that quantum Hall wave functions for Jain series ground states can be exactly represented using conformal field theory, linking CF phenomenology with algebraic and topological insights.

Contribution

It introduces a conformal field theory framework to express composite fermion wave functions and quasiparticle states, providing new algebraic and topological understanding.

Findings

Exact CFT representation of Jain series wave functions

Algebraic description of quasiparticles and quasiholes

Topological properties elucidated through correlators

Abstract

We show that the quantum Hall wave functions for the ground states in the Jain series can be exactly expressed in terms of correlation functions of local vertex operators, V_n, corresponding to composite fermions in the n:th composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions.