Understanding the 5/2 Fractional Quantum Hall Effect without the Pfaffian Wave Function

TL;DR

This paper shows that the 5/2 fractional quantum Hall effect can be explained using composite fermion theory without the Pfaffian wave function, emphasizing residual interactions and systematic improvements.

Contribution

It introduces a composite fermion-based approach to understand the 5/2 FQHE without relying on the Pfaffian wave function, enabling systematic perturbative analysis.

Findings

Achieves understanding of 5/2 FQHE without Pfaffian wave function.

Highlights the importance of residual interactions between composite fermions.

Provides a framework for calculating ground and excited states systematically.

Abstract

It is demonstrated that an understanding of the 5/2 fractional quantum Hall effect can be achieved within the composite fermion theory without appealing to the Pfaffian wave function. The residual interaction between composite fermions plays a crucial role in establishing incompressibility at this filling factor. This approach has the advantage of being amenable to systematic perturbative improvements, and produces ground as well as excited states. It, however, does not relate to non-Abelian statistics in any obvious manner.