We study the ground-state critical behavior of the Bose-Hubbard model in two and three dimensions at large filling factors, using the quantum spherical model as the primary analytical framework. The scaling properties of the critical hopping amplitude $t$ at the quantum phase transition from the Mott insulator to the superfluid phase are analyzed in detail. We derive the scaling behavior of $t$ as a function of interaction strength and chemical potential and validate our results through comparisons with the process chain approach, demonstrating consistency and robustness across methods. Our findings reveal dimensional dependencies and significant deviations in the scaling behavior at high filling factors compared to low filling regimes, underscoring the impact of quantum fluctuations in these systems. The results offer a comprehensive understanding of the universality classes and phase diagram structures of the Bose-Hubbard model at high occupancies, contributing to the broader study of strongly correlated bosonic systems.

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• Bose gases
• Bose-Einstein condensates
• Cold atoms & matter waves
• Cold gases in optical lattices