Abstract
The critical Landau-level filling factor for the transition from Laughlin's liquid state to a Wigner crystal is determined by comparing the energies of these states. The Wigner-crystal energy is substantially improved over the Hartree-Fock result by using a variational wave function which includes particle correlations. The liquid-state energy is obtained from the Monte Carlo calculation of Levesque, Weis, and Mac-Donald. We find to be slightly larger than ? which is consistent with the experimental observation by Mendez and co-workers that the fractional quantum-Hall effect does not occur for . The improvement in the crystal energy by correlation is essential to this agreement since without correlations, . In addition the crystal correlation energy explains the very low temperatures required to see the liquid state.
- Received 3 April 1984
DOI:https://doi.org/10.1103/PhysRevB.30.473
©1984 American Physical Society