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The interplay between charge and spin degrees of freedom in stronglycorrelated fermionic systems, in particular of Dirac fermions, is along-standing problem in condensed matter physics. We investigate the competingorders in the half-filled SU(2N) Hubbard model on a honeycomb lattice, whichcan be accurately realized in optical lattices with large-spin ultra-coldalkaline-earth fermions. Employing large-scale projector determinant quantumMonte Carlo simulations, we have explored quantum phase transitions from thegapless Dirac semi-metals to the gapped Mott-insulating phases in the SU(4) andSU(6) cases. Both of these Mott-insulating states are found to be columnarvalence bond solid (cVBS) and to be absent of the antiferromagnetic Neelordering and the loop current ordering. Inside the cVBS phases, the dimerordering is enhanced by increasing fermion components and behavesnon-monotonically as the interaction strength increases. Although thetransitions generally should be of first order due to a cubic invariancepossessed by the cVBS order, the coupling to gapless Dirac fermions can softenthe transitions to second order through a non-analytic term in the free energy.Our simulations provide important guidance for the experimental exploration ofnovel states of matter with ultra-cold alkaline earth fermions.

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