Quantum Monte Carlo Simulations of the SU(N) Hubbard Model

The rich physics of the SU(N) Fermi-Hubbard model (FHM) has been investigated in recent years with experiments using alkaline-earth-like atoms in optical lattices. It is anticipated that these models, which have enhanced symmetry and large spins, will display unique and intriguing phase diagrams with phases that depend intricately on N. By directly observing long-range correlations, experimentalists will be able to distinguish between finite temperature analogs of the range of proposed magnetic phases thanks to the current advancements in quantum gas microscopes. Understanding the finite-temperature phase diagrams in the 2D square lattice is essential for all of these experimental endeavors, especially for identifying finite-temperature signals of such fascinating physics. 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 discuss the model's thermodynamic and magnetic properties for different values of N as a function of temperature and chemical potential.