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Physical review. B, Condensed matter

Jastrow-Slater trial wave functions for the fractional quantum Hall effect: Results for few-particle systems

Gautam Dev, Jainendra K. Jain

Published Jan 15, 1992• 84 citations
Publisher

Abstract

We report results of a numerical study of the Jastrow-Slater trial wave functions for the fractional quantum Hall effect proposed by one of us. We study systems of up to eight electrons and find that these trial states are an extremely good approximation to the true Coulomb states.
DOI
10.1103/physrevb.45.1223

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Trial wave functions which, in the thermodynamic limit, describe states relevant to the fractional quantum Hall effect are explicitly constructed for up to eight electrons. Estimates are given for the ground-state energies and pair-correlation functions and for the low-lying excitation energies for states associated with the filling factors \ensuremath{\nu}=(1/3), (2/7), and (2/5). The results help explain why the filling factors \ensuremath{\nu}=${\ensuremath{\nu}}_{m}$=m/(2m+1), m=1,2,..., and \ensuremath{\nu}=1-${\ensuremath{\nu}}_{m}$ show strong quantum Hall effects.
New microscopic trial wave functions are proposed for fractional quantized Hall states at $\ensuremath{\nu}=\frac{2}{(2p+1)}$. Results for $\ensuremath{\nu}=\frac{2}{5} \mathrm{and} \frac{2}{7}$ based on Monte Carlo and exact numerical computations are presented. For $N\ensuremath{\le}10$ electrons on a sphere, energies differ from the exact ground-state energy by less than 0.3%. For even ppp, such as $\ensuremath{\nu}=\frac{2}{5}$, the trial wave function may be regarded as a microscopic realization of the condensed quasiparticle state postulated in hierarchical schemes.