Size dependence in small-system calculations for fractional quantum Hall states.

Abstract

We discuss the size dependence of small-system periodic-boundary-condition calculations of ground-state energies and excitation energies for two-dimensional electron systems in a strong magnetic field. The discussion is based on an examination of the Hartree-Fock approximation for a finite-size system. We find that finite-size-system calculations overestimate the magnitude of the ground-state energy and underestimate excitation energies, especially in the case of higher-orbital Landau levels. Numerical estimates of the finite-size corrections are given for 4-, 9-, and 16-electron systems.