The attractive SU(N) Fermi-Hubbard model: New phases in ultracold molecules

Since the early days of ultracold quantum gases, SU(N)-symmetric extensions of typical many-body models have been used to describe the many hyperfine states in ultracold atoms. In particular, alkaline-earth atoms in optical lattices have been well-described by the repulsive SU(N) Fermi-Hubbard model and used as a fruitful quantum simulation platform for this model. Motivated by the advances made in recent experiments with shielding in ultracold molecules - which has been shown to lead to an SU(N) symmetry with tunable repulsive and attractive interactions - we have used a Determinant Quantum Monte Carlo method to study the attractive SU(N) Fermi-Hubbard model on a 2D square lattice at finite temperature. The attractive SU(N) Fermi-Hubbard model hosts a range of interesting new physics unavailable in other ultracold matter, including novel ordered phases and multi-particle bound states. We investigate the formation and ordering of three-particle "trions" in the SU(3) case, including a finite-temperature phase transition that does not exist in the SU(2) case. We also study evidence of BCS pairing "color superfluid" phases and consider the feasibility of observing these phases in an ultracold molecule experiment. Finally, we discuss the advantages of considering the attractive model both as a model of interesting new physics and as a computationally-efficient way to treat many-component systems.