Abstract
A self-consistent equation is derived for the order parameter of quantum phases in an optical lattice within a mean-field approximation to the Bose–Hubbard model. Analyzing the solutions of the self-consistent equation in terms of the number fluctuations of quasiparticles, the one-body density matrix of atoms, and the normalized correlation function of quasiparticles, we have identified two types of Mott-insulator phases that are characterized by different values of the order parameter, quasiparticle fluctuations, and correlations. We have also identified the quantum critical points separating these two types of Mott-insulator phases and the corresponding quantum critical lines on the phase diagram.
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