Topological Structure and an Accurate Wave Function for the Enigmatic 5/2 Fractional Quantum Hall State

TL;DR

This paper analyzes the topological structure of the 5/2 fractional quantum Hall state, constructing an accurate wave function that incorporates multiple graph-based contributions, revealing complex clustering behavior.

Contribution

It introduces a comprehensive graph-based basis for the ground state wave function at 5/2 filling, including contributions beyond the Pfaffian, for Coulomb interactions.

Findings

The wave function supports clustering up to half of the composite bosons.

Multiple graphs contribute to the exact ground state, not just the Pfaffian.

Supports strong-coupling regime with clustering phenomena.

Abstract

We comprehensively show the topological structure--order of zeros felt by an electron at the positions of other electrons --for the enigmatic filling factor 5/2 at the "Pfaffian-shift" in a spherical geometry. A set of linearly independent antisymmetric functions that are constructed from the possible graphs preserving this topological structure provides complete basis for determining an accurate ground state wave function for any interaction, in particular the Coulomb interaction. One of the graphs describes $Z_2$ para-fermion equivalently the Pfaffian wave function, but some of the other graphs also contribute to form the exact ground state for the Coulomb interaction. We further show that our wave function for the Coulomb interaction supports clustering up to half of the composite bosons, signifying a strong-coupling regime.