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Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions

The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with large-spin ultra-cold alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semi-metals to the gapped Mott-insulating phases in the SU(4) and SU(6) cases. Both of these Mott-insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic Neel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves non-monotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a non-analytic term in the free energy. Our simulations provide important guidance for the experimental exploration of novel states of matter with ultra-cold alkaline earth fermions.