Charge and Statistics of Quantum Hall Quasi-Particles. A numerical study of mean values and fluctuations

TL;DR

This study uses Monte Carlo simulations to analyze charge expectations and fluctuations of quasi-particles in quantum Hall systems, comparing different wave functions and calculating their statistical properties.

Contribution

It provides a detailed numerical comparison of charge and fluctuation properties of various quantum Hall quasi-particles, including new Berry phase calculations for Jain's quasi-electron.

Findings

Charge values match theoretical expectations (-1/3 and 1/3 of electron charge).

Charge fluctuations are negligible for quasi-holes and Jain quasi-electrons, but not for Laughlin quasi-electrons.

Jain quasi-electron exhibits more stable statistics parameters than Laughlin quasi-electron.

Abstract

We present Monte Carlo studies of charge expectation values and charge fluctuations for quasi-particles in the quantum Hall system. We have studied the Laughlin wave functions for quasi-hole and quasi-electron, and also Jain's definition of the quasi-electron wave function. The considered systems consist of from 50 to 200 electrons, and the filling fraction is 1/3. For all quasi-particles our calculations reproduce well the expected values of charge; -1/3 times the electron charge for the quasi-hole, and 1/3 for the quasi-electron. Regarding fluctuations in the charge, our results for the quasi-hole and Jain quasi-electron are consistent with the expected value zero in the bulk of the system, but for the Laughlin quasi-electron we find small, but significant, deviations from zero throughout the whole electron droplet. We also present Berry phase calculations of charge and statistics parameter for the Jain quasi-electron, calculations which supplement earlier studies for the Laughlin quasi-particles. We find that the statistics parameter is more well behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron.