Analysis of the fractional-quantum-Hall-effect ground state in the symmetric gauge

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Abstract
We present a systematic analysis of the fractional-quantum-Hall-effect (FQHE) Hamiltonian in the symmetric gauge and of the Laughlin wave function (LWF). As in the Landau Gauge, it turns out that the ground state (g.s.) is dominated by a multiple-drop parent state composed of drops of constant actual size (the number of electrons in a given drop thus depends on the distance between adjacent Landau orbitals). These drops are further diffused by correlation effects in order to obtain the g.s. We check the accuracy of the LWF to describe this behavior for one-drop parent states (i.e., the situation for less than six particles) but we find that it overestimates correlation effects when more electrons are present. We correct some of the failures of the LWF but others are hard to eradicate without drastic changes, and so we propose a new approximant for the FQHE g.s. Our proposal allows an easy comprehension of the ground state of unpolarized FQHE systems, the ground-state crystallization effect, and the excitation characteristics.