Comment on 'Ground state energy of the fractional quantised Hall system'

Abstract

For original paper see ibid., vol.17, L419 (1984). Recently Tao (1984b) has given results of a perturbation description of the anomalous quantum Hall systems, which seem to cast doubt on some of Laughlin's (1983) insights. This doubt is the result of a misleading presentation of results and is not warranted. The minimum possible Coulomb interaction energy of a two-dimensional electron gas (2DEG) is the energy of the Wigner crystal, EWC. EWC is therefore a lower bound on the contribution of the electron-electron interaction to the ground-state energy, EGS. In a magnetic field the kinetic energy basis is discrete and is made up of Landau levels. If for a filling factor nu <1 the contribution of all except the lowest Landau level can be neglected, then the kinetic energy is constant. The ground-state energy is just the minimum interaction energy evaluated subject to the restriction that electrons occupy states in the lowest Landau level only. This energy is of course still higher than EWC (Yoshioka and Lee 1983). Tao (1984b) has given ground-state energies measured from h omega c/2 per electron which, for nu =1/4, 1/5, 1/6 are lower than this absolute lower bound. The author shows that the result of Tao's perturbation theory is clearly not an upper bound and therefore should not be compared as such with Laughlin's variational result for any value of nu . Unfortunately Tao makes this comparison.