A comparison of FQHE quasi electron trial wave functions on the sphere

TL;DR

This paper compares different trial wave functions for quasiparticles in the fractional quantum Hall effect on a spherical geometry, evaluating their accuracy against exact numerical solutions for small electron systems.

Contribution

It provides a detailed comparison of Haldane's and Jain's quasiparticle wave functions on the sphere, assessing their effectiveness at filling factor 1/3.

Findings

Haldane's and Jain's wave functions show varying degrees of agreement with exact diagonalization.

Energy expectation values closely match for certain trial states.

Pair angular momentum distributions reveal differences in quasiparticle descriptions.

Abstract

We study Haldane's and Jain's proposals for the quasiparticle wave function on the sphere. The expectation values of the energy and the pair angular momenta distribution are calculated at filling factor 1/3 and compared with the data of an exact numerical diagonalization for up to 10 electrons with Coulomb and truncated quasipotential interaction.