Magnetic and Charge Order in the SU(N) Hubbard Model

The SU(N) Fermi-Hubbard model has been investigated with experiments using alkaline-earth-like atoms in optical lattices. With enhanced symmetry, it is anticipated to display unique and intriguing phase diagrams with charge and spin ordering that depend intricately on N, while the effects brought by thermal fluctuations remain to be explored theoretically. In this presentation, we discuss our progress in developing a finite temperature quantum Monte Carlo code for the SU(N) FHM in which we mitigate the sign problem by performing the constrained path approximation. We first provide benchmarks against exact diagonalization and then discuss the model's thermodynamic and magnetic properties as a function of temperature and chemical potential, including the formation of exotic magnetic ordering and emergence of entropy-driven phenomena such as the Pomeranchuk effect.