Universal probes for antiferromagnetic correlations and entropy in cold fermions on optical lattices

Abstract

We determine antiferromagnetic (AF) signatures in the half-filled Hubbard model at strong coupling on a cubic lattice and in lower dimensions. Upon cooling, the transition from the charge-excitation regime to the AF Heisenberg regime is signaled by a universal minimum of the double occupancy at entropy $s\ensuremath{\equiv}S/(N{k}_{\text{B}})={s}^{*}\ensuremath{\approx}\mathrm{ln}(2)$ per particle and a linear increase of the next-nearest-neighbor (NNN) spin correlation function for $s<{s}^{*}$. This crossover, driven by a gain in kinetic exchange energy, appears as the essential AF physics relevant for current cold-atom experiments. The onset of long-range AF order (at low $s$ on cubic lattices) is hardly visible in nearest-neighbor spin correlations versus $s$, but could be detected in spin correlations at or beyond NNN distances.