Charge and statistics of quantum Hall quasi-particles — a numerical study of mean values and fluctuations Original Research Article

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 Jainʹs definition of the quasi-electron wave function. The considered systems consist of from 50 to 200 electrons, and the filling fraction is 13. For all quasi-particles our calculations reproduce well the expected values of charge; −13 times the electron charge for the quasi-hole, and 13 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, calculated as a function of distance, is more well behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron. However, the sign of the parameter is opposite of what is expected from qualitative arguments.