Simple $N$-scaling above the superexchange energy of thermodynamic observables in the SU($N$) Fermi Hubbard Model at $1/N$ filling in the two dimensional square lattice

The SU(2) symmetric Fermi Hubbard model (FHM) plays an essential role in the understanding of strongly correlated fermionic many-body systems. When the system is in the one particle per site and strongly interacting limit $U/t \gg 1$, it is effectively described by the Heisenberg Hamiltonian. In this limit, extending the typical SU(2) symmetry to SU(N) is predicted to give exotic phases of matter in the ground state, with complicated dependence of the ground state on $N$. The question we address in this talk is whether the situation is similarly complicated at $T$ at and above the superexchange energy. To answer this question we numerically explore the SU($N$) FHM in a two-dimensional square lattice using determinant Quantum Monte Carlo and Numerical Linked Cluster Expansion. Our main finding is that for temperatures above the superexchange energy, where the different $N$ systems are just dominated by short-range correlations, the energy, double occupancy, and kinetic energy collapse upon a simple rescaling with $1/N$. Although the physics in the regime studied is well beyond that captured by low-ordered high-temperature series, we show that an analytic description of the scaling is possible in terms of only one- and two-site correlations.