Solving the SU($N$) Orbital Hatsugai-Kohmoto Model

We show that the physics of the SU($N$) Hubbard model can be realistically simulated with the recently developed orbital Hatsugai-Kohmoto model. In this approach, the momentum mixing absent from the band Hatsugai-Kohmoto model is included by grouping $n$-Hubbard atoms into a cluster. We take advantage of the rapid convergence of this scheme ($1/n^2$) and show that for $n\approx O(10)$, quantitative agreement with the determinantal quantum Monte Carlo method arises for the double occupancy as well as qualitative agreement for the filling and compressibility across the Mott transition. Additional features of this work are that we can obtain low-temperature physics, which could be qualitatively different from its high-temperature counterpart, and dynamical quantities without resorting to analytical continuation, thereby establishing the orbital Hatsugai-Kohmoto model as a useful alternative perspective for studying strong correlations in SU($N$) systems.