Numerical study of charge and statistics of Laughlin quasi-particles

TL;DR

This paper uses numerical methods to analyze the charge and statistical properties of Laughlin quasi-particles near filling fraction 1/3, revealing detailed behaviors and convergence patterns for quasi-holes and quasi-electrons.

Contribution

It provides the first detailed numerical analysis of quasi-electron charge and statistics, highlighting finite size effects and the need for singular wave functions for quasi-electrons.

Findings

Quasi-hole charge confirmed as e/3 and statistics as 1/3.

Quasi-electron charge approaches -e/3 with finite size corrections.

Quasi-electron statistics may converge to 1/3, sharing the same sign as quasi-holes.

Abstract

We present numerical calculations of the charge and statistics, as extracted from Berry phases, of the Laughlin quasi-particles, near filling fraction 1/3, and for system sizes of up to 200 electrons. For the quasi-holes our results confirm that the charge and statistics parameter are $e/3$ and 1/3, respectively. For the quasi-electron charge we find a slow convergence towards the expected value of $-e/3$, with a finite size correction for $N$ electrons of approximately $-0.13e/N$. The statistics parameter for the quasi-electrons has no well defined value even for 200 electrons, but might possibly converge to 1/3. Most noteworthy, it takes on the same sign as for the quasi-holes, due to terms that have previously been ignored. The anyon model works well for the quasi-holes, but requires singular two-anyon wave functions for modelling two Laughlin quasi-electrons.