More about the Laughlin droplet

TL;DR

This paper compares the exact ground state wave function of a 2D electron droplet in a magnetic field with the Laughlin ansatz at filling factor 1/3, observing decreasing overlap as electron number increases.

Contribution

It provides a detailed comparison between exact diagonalization results and the Laughlin wave function for larger electron systems.

Findings

Overlap decreases with increasing electron number

Laughlin ansatz becomes less accurate for larger droplets

Insights into the limitations of the Laughlin wave function

Abstract

We compare the exact diagonalization ground wave function (calculated wothout any restriction) of a two dimensional droplet submitted to a perpendicular magnetic field with the Laughlin ansatz as the number of electrons increases. The fully polarized case for filling factor 1/3 without lateral confining potential or Zeeman effect is considered. We observe that the overlap worsens as the number of electrons increases.