Ground State Properties of SU(4) Attractive Hubbard Model on a Honeycomb Lattice

We study the competing orders in the SU(4) attractive Hubbard model on a honeycomb lattice, which can be realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing determinant quantum Monte Carlo (DQMC) simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the charge density wave order at half filling. Doping away from half filling, which is still sign-problem-free in DQMC, we investigate the competitions between pairing orders and quartetting orders, where the quartetting order is a four-fermion counterpart of the Cooper pairing.