A new hypernetted-chain treatment for Laughlin quantum Hall states

The hypernetted-chain theory is applied to study the fractional quantum Hall effect with the Laughlin wave functions. A new method is proposed to include the effect of the elementary diagrams, which improves upon the commonly used modified hypernetted-chain approximation. The correlation energy, the pair distribution function, as well as the magnetoroton excitation spectrum have been computed within this method. The results obtained are in very good agreement with the available Monte Carlo estimates. The method is generalizable to treat other wave functions, like those corresponding to the hierarchical states or those of composite fermion type.