Published Paper Details:

In this study, the quantum phase transitions in the SU(2N) Hubbard model on a honeycomb lattice. We focus on how Dirac fermions shift from a gapless semimetal to a Mott-insulating phase. Using quantum Monte Carlo (QMC) simulations, we analyzed SU (4) and SU (6) systems and found a columnar valence bond solid (cVBS) phase. Our results showed that fermion interactions drive spontaneous symmetry breaking, forming dimerized states. The transition, which is expected to be first-order, appears second-order owing to quantum fluctuations. We extract critical exponents and confirm that the transition follows Gross-Neveu universality. A key finding was the non-monotonic dimer order. At intermediate U, the dimer strength increases but weakens at high U, suggesting competing phases. These results apply to ultracold alkaline-earth atoms, where SU(N) symmetry appears naturally. Future work should explore larger N values, finite-size scaling, and non-Hermitian extensions. This study improves our understanding of strongly correlated Dirac fermion systems, the bridging theory and experiment in quantum materials.