Bose-Hubbard Model on a Honeycomb Superlattice: Quantum Phase Transitions and Lattice Effects

We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\Delta/t$ and the onsite interaction $U/t$ gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance-double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.