Solving SU(N) orbital Hatsugai-Kohmoto Model for ultracold atoms

The SU(N>2) Hubbard model has gained significant interest due to its realization in ultracold atom systems, allowing the exploration of exotic quantum phases beyond the conventional SU(2) model and yielding a much richer phase diagram. However, the increased number of spin components and strong correlations make the numerical simulation of this model computationally demanding. A recent study demonstrated that orbital extensions of the exactly solvable Hatsugai-Kohmoto (HK) model can efficiently simulate the SU(2) Hubbard model. First, we show that the band HK SU(N>2) model is exactly solvable. Secondly, we use the orbital framework to solve the SU(N>2) model. By benchmarking our results with determinant quantum Monte Carlo at high temperatures for SU(3) and SU(4) Hubbard models, we investigate low-temperature spectral properties and potential magnetic ordering with one particle per site. Our findings provide a foundation for studying doped SU(N>2) Mott insulators.