Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on the correlated basis functions of the composite-fermion theory, that allows a systematic improvement of the wave functions and the energies for low-lying eigenstates. For a test of the method, we study systems for which exact results are known, and find that practically exact answers are obtained for the ground state wave function, ground state energy, excitation gap, and the pair correlation function. We show how the perturbative scheme helps resolve the subtle physics of competing orders in certain anomalous cases.
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