Interaction-driven crossover from Mott insulator–superfluid criticality to Bose-Einstein condensation in a simple cubic lattice

We investigate how strongly interacting bosons, described by the Bose-Hubbard Hamiltonian, transition from the Mott insulator to the superfluid phase and, ultimately, to a regime of vanishing interaction where the system smoothly transitions to an ensemble of free bosons undergoing Bose-Einstein condensation. Our study focuses on bosons residing on a three-dimensional simple cubic lattice, with tight-binding interactions characterized by the kinetic energy $t$ between neighboring lattice sites and on-site repulsion $U$. To achieve this, we develop a formalism based on mapping the original quantum mechanical Hamiltonian onto an effective quantum spherical model. This approach is nonperturbative in interaction energy and spans the entire range of the interaction parameter $U$. Our findings are presented through a series of multiparameter phase diagrams that include temperature, interaction energy, chemical potential, and particle density, highlighting the corresponding critical surfaces and lines. In this context, we address the issue of quantum critical points at fixed densities, which appear as endpoints in the temperature-interaction phase diagram. We also compare our theoretical results, where applicable, with other approaches, including quantum Monte Carlo simulations.