Recent advances in microwave shielding have increased the stability and control of large numbers of polar molecules, allowing for the first realization of a molecular Bose-Einstein condensate. Remarkably, it was also recently realized that shielded polar molecules exhibit an $\mathrm{SU}(N)$ symmetry among their hyperfine states, opening the door to $\mathrm{SU}(N)$ systems with larger $N$, bosonic particle statistics, and tunable interactions—both repulsive and attractive. Motivated by these results, we have studied the SU(3) attractive Fermi-Hubbard model (FHM) on a square lattice. Using the determinant quantum Monte Carlo (DQMC) method, we explore the finite temperature phase diagram and provide evidence for three distinct regions—a three-component Fermi liquid (FL) region, a “trion” liquid (TL) region, and an ordered charge density wave (CDW) phase. The CDW phase is stable at finite temperature [in contrast to the SU(2) CDW], while the FL to TL crossover appears to point to a quantum phase transition at zero temperature. Our method extends straightforwardly to larger $N$ and is sign problem free for even values of $N$. With these results, we demonstrate the potential physics enabled by using polar molecules as a quantum simulation platform for the attractive $\mathrm{SU}(N)$ FHM.

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• Cold and ultracold molecules
• Cold gases in optical lattices
• Hubbard model
• Quantum Monte Carlo