The Attractive SU(N) Fermi-Hubbard Model in Ultracold Molecules

The SU(N) Fermi-Hubbard model has seen a surge of interest due to its realization in alkaline-earth atoms in optical lattices. It has a rich, exotic phase diagram resulting from its high symmetry. However, the alkaline-earth atoms have limitations: in particular, they lack magnetic Feshbach resonances, so can realize only repulsive SU(N) Fermi-Hubbard models. Motivated by our (unpublished) work showing that shielded ultracold molecules enjoy an SU(N) symmetry with more flexible interactions, we study the attractive SU(N) Fermi-Hubbard model. By using the Determinant Quantum Monte Carlo (DQMC) method with an appropriate Hubbard-Stratonovich transformation, we can accurately calculate properties of this model. While our method works for arbitrary N, we have focused in particular on the square-lattice SU(3) model. We have studied the formation and ordering of three-particle bound states of SU(3) singlets with density, temperature, and interaction strength. We make predictions for experiments and suggest the most exciting directions forward.