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

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_{e}=6 electrons at the filling factor ν=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_{e}=7 electrons at ν=1/3. Moreover, similar exact results are derived at the filling ν=1/5 for systems with up to N_{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.

Keywords

• quantum Hall effect
• 2D electron gas
• many-body wave function
• strongly correlated system