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 authors study thermodynamic properties of the SU(
N) Fermi-Hubbard model in 2D square lattices and discover simple scaling laws of the energy, the number of on-site pairs, and the kinetic energy with respect to
N when the temperature is above the superexchange energy. The results establish a limit to the cooling for SU(
N) fermions in 2D, in contrast to the arbitrarily low temperatures that could potentially be achieved in 1D.
We investigate the thermodynamic properties of a half-filled SU(2N) Hubbard model in the two-dimensional square lattice by the method of the determinant 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 in the case of SU(6). Various physical quantities including entropy, charge fluctuations, and spin correlations are calculated.
The ground state of the hard-core Fermi-Hubbard model with a single hole (and otherwise half-filled) is a ferromagnet on the square lattice, but an antiferromagnet on the triangular lattice, as those spin patterns minimize the kinetic energy of the hole. What is the magnetic behavior as one interpolates between these two geometries? Using a sophisticated quantum Monte Carlo algorithm, the authors determine here the magnetic correlations as the lattice is varied. Their calculations are performed in the thermodynamic limit and at temperatures comparable to current cold-atom experiments. They find a magnetic crossover between the two geometries, and calculate signatures of it that are observable in these experiments.