Monte Carlo evaluation of trial wave functions for the fractional quantized Hall effect: Disk geometry.

Abstract

Monte Carlo methods have been employed to evaluate the energy of two previously proposed trial wave functions for the quasiparticle at the $\ensuremath{\nu}=\frac{1}{3}$ quantized Hall state of the two-dimensional electron system. The two wave functions have the same energy within our statistical accuracy, and are consistent with a value ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{+}(\frac{1}{3})\ensuremath{\approx}\frac{(0.073\ifmmode\pm\else\textpm\fi{}0.008){e}^{2}}{\ensuremath{\epsilon}{l}_{o}}$, where ${l}_{0}$ is the magnetic length, and $\ensuremath{\epsilon}$ the background dielectric constant. Simulations of the quasihole state confirm previous estimates of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{\ensuremath{-}}(\frac{1}{3})\ensuremath{\approx}\frac{0.026{e}^{2}}{\ensuremath{\epsilon}{l}_{0}}$. We have also studied the charge distributions of the quasiparticle and quasihole states, and we have evaluated the energies of a previously proposed microscopic trial wave function for the ground state at $\ensuremath{\nu}=\frac{2}{5}, \frac{2}{3}, \mathrm{and} \frac{2}{7}$.