Composite Particle Formation and Ordering in the SU(N) Fermi-Hubbard Model

SU(N)-symmetric extensions of important many-body models have been realized in ultracold matter. The repulsive SU(N) Fermi-Hubbard model has been realized using alkaline-earth atoms, which have served as a fruitful quantum simulation platform for this model. Motivated by shielded ultracold molecules, which have recently been shown to lead to an SU(N) symmetry, and allow tunable repulsive and attractive interactions, we use Determinant Quantum Monte Carlo to study the attractive SU(N) Fermi-Hubbard model on a 2D square lattice at finite temperature. We show that 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. Near half-filling, we have observed a Charge Density Wave (CDW) phase which is stable at finite temperature (unlike the familiar N=2 case), and evidence of a quantum phase transition driven by the formation of composite particles. We have studied the interface between this CDW phase and regimes with and without composite particles for multiple values of N. We also consider BCS pairing "color superfluid" phases and the feasibility of observing them in an ultracold molecule experiment.