Thermodynamic properties of the SU($2N$) ultra-cold fermions in optical lattices

We investigate the thermodynamic properties of a half-filled SU($2N$) Fermi-Hubbard model in the two-dimensional square lattice using the determinantal quantum Monte Carlo simulation, which is free of the fermion ``sign problem''. The large number of hyperfine-spin components enhances spin fluctuations, which facilitates the Pomeranchuk cooling to temperatures comparable to the superexchange energy scale at the case of SU$(6)$. Various quantities including entropy, charge fluctuation, and spin correlations have been calculated.