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

Monte Carlo methods have been employed to evaluate the energy of two previously proposed trial wave functions for the quasiparticle at the $\nu =\frac{1}{3}$ 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 ${\tilde{\varepsilon }}_{+}\left(\frac{1}{3}\right)\approx \frac{(0.073\mathrm{}\pm 0.008)e^2}{\epsilon l_o}$, where $l_0$ is the magnetic length, and $\epsilon$ the background dielectric constant. Simulations of the quasihole state confirm previous estimates of ${\tilde{\varepsilon }}_{-}\left(\frac{1}{3}\right)\approx \frac{0.026e^2}{\epsilon l_0}$. 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 $\nu =\frac{2}{5}, \frac{2}{3}, \mathrm{and} \frac{2}{7}$.