We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments.
Baoming Tang, Thereza Paiva, Ehsan Khatami, and Marcos Rigol. "Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice" Physical Review Letters (2012). doi:10.1103/PhysRevLett.109.205301