Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

TL;DR

This paper develops an analytic framework for calculating hierarchical and composite fermion wave functions in the fractional quantum Hall effect on a sphere, demonstrating their near-perfect overlap and physical equivalence.

Contribution

It introduces a new analytic method using projective coordinates to compare hierarchical and composite fermion wave functions on the sphere.

Findings

Overlaps between the two wave functions are nearly one.

Hierarchical and composite fermion theories are shown to be physically equivalent.

Framework facilitates analytic calculations in fractional quantum Hall studies.

Abstract

We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are all most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory and the composite fermion theory, are physically equivalent.