SU($N$) alkaline-earth fermions in optical lattices: thermodynamics and magnetism.

Our recent observation of nearest-neighbor antiferromagnetic (AFM) spin-correlations in an SU(6) $^{173}$Yb Fermi gas loaded in 1D, 2D, and 3D optical lattices, opens new questions about strongly correlated systems\footnote{S. Taie, et. al., arXiv:2010.07730}. Two major questions are how long-range correlations form, and what happens when the system is doped away from the Mott insulating regime. We report progress towards answering these questions. In our previous work, we calculated the experimentally measured properties and found that the nearest-neighbor AFM correlations agree quantitatively with no fitting for all temperatures in 1D, and at temperatures where converged theoretical results can be obtained in 3D. In 1D, experiments reached the lowest $k_BT/t$ ever reported for a Fermi gas in an optical lattice. These results lay the foundation for our ongoing studies of long-ranged magnetism and doped Mott insulators. We numerically study the thermodynamics and magnetism of the SU($N$) Fermi Hubbard as a function of $N$, $U$, and $T$ in 2D at unit-filling using determinant Quantum Monte Carlo. Our results are experimentally relevant, since experiments are now poised to discriminate finite temperature analogs of theoretically proposed ground states using quantum gas microscopy.