Fusion & Tensoring of Conformal Field Theory and Composite Fermion Picture of Fractional Quantum Hall Effect

TL;DR

This paper introduces a conformal field theory framework to describe quantum Hall transitions, using fusion and tensoring of theories to recover Jain's composite fermion picture and explain fractional quantum Hall states.

Contribution

It presents a novel conformal field theory approach employing fusion and tensoring to model quantum Hall transitions and fractional states, unifying various observed fractions.

Findings

Reproduces Jain's flux attachment picture via fusion rules.

Describes higher Landau levels through tensor products of conformal theories.

Identifies a critical exponent 7/3 matching experimental observations.

Abstract

We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of non-unitary theories, we explicitly recover Jain's picture of attaching flux quanta by the fusion rules of primary fields. Filling higher Landau levels of composite fermions can be described by taking tensor products of conformal theories. The usual projection to the lowest Landau level corresponds then to a simple coset of these tensor products with several U(1)-theories divided out. These two operations -- the fusion map and the tensor map -- can explain the Jain series and all other observed fractions as exceptional cases. Within our scheme of transitions we naturally find a field with the experimentally observed universal critical exponent 7/3.