STUDY ON THE MOST PROBABLE DISTRIBUTION FOR LAUGHLIN WAVE FUNCTIONS

We show that, up to a global phase freedom, the most probable distribution of electrons given by the maxima of modulus square of Laughlin wave function (LWF), which is known to be a wave function for an incompressible liquid state of fractional Hall effect, has a triangular lattice structure. We introduce the Gaussian approximation for the modulus square of LWF. We find that the radial distribution function calculated from the Gaussian approximation has a form close to that of LWF at ν = 1, 1/3 and close to a crystal-like behavior when ν becomes smaller. We interprete the underlying physics to be that in the incompressible liquid regime, the "hidden" triangular lattice is smeared away by the quantum phase fluctuation, and as a precursor for liquid-crystal transition when the filling ν decreases towards the crystallization regime, it might manifest itself to be a sort of correlated short-range ordered density fluctuation.