Method of computation of energies in the fractional quantum Hall effect regime

TL;DR

This paper extends exact energy calculations for fractional quantum Hall systems to larger electron numbers and different filling factors, providing computational details and validating results with Monte Carlo methods.

Contribution

It introduces an extended computational approach for calculating energies in FQHE regimes, including larger systems and additional filling factors, with analytical results corroborated by Monte Carlo methods.

Findings

Exact energies for N=7 electrons at ν=1/3

Exact energies for N=6 electrons at ν=1/5

Good agreement with Monte Carlo results

Abstract

In a previous work, we reported exact results of energies of the ground state in the fractional quantum Hall effect (FQHE) regime for systems with up to $N_{\text{e}} = 6$ electrons at the filling factor $\nu = 1/3$ by using the method of complex polar coordinates. In this work, we display interesting computational details of the previous calculation and extend the calculation to $N_{\text{e}} = 7$ electrons at $\nu = 1/3$. Moreover, similar exact results are derived at the filling $\nu = 1/5$ for systems with up to $N_{\text{e}} = 6$ electrons. The results that we obtained by analytical calculation are in good agreement with their analogues ones derived by the method of Monte Carlo in a precedent work.