\title{Double occupancy as a universal probe for antiferromagnetic correlations\\
       and entropy in cold fermions on optical lattices}

     % We study the dimensional dependence of  the double occupancy $D$ using dynamical mean-field theory, direct quantum Monte Carlo (in dimensions $d=2,3$), and Bethe Ansatz (in $d=1$), and establish $D$ as a local probe of antiferromagnetic (AF) correlations. As a function of entropy $s=S/(N k_{\text{B}})$, $D$ is nearly universal with respect to dimension; the minimum in $D(s)$ approaches $s\approx \log(2)$ at strong coupling. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve $s<\log(2)/2$ and should consider lower dimensions, for which the AF effects are larger.

% We demonstrate that the signatures of antiferromagnetic (AF) correlations in the double occupancy $D$ persist in all dimensions down to $d=1$, therefore establishing $D$ as a local probe of AF correlations. As a function of entropy $s=S/(N k_{\text{B}})$, $D$ is nearly universal with respect to dimension; the minimum in $D(s)$ approaches $s\approx \log(2)$ at strong coupling, also marking the applicability limit of spin models. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve $s<\log(2)/2$ and should consider lower dimensions, for which the AF effects are larger. \nb{$D$ measurable! unique AF signature almost within current $s$ reach, new: weak coupling, cubic $T_N$ nonuniversal (sc vs.\ bcc) }

We study antiferromagnetic (AF) order and correlations in the half-filled Hubbard model using dynamical mean-field theory, determinantal quantum Monte Carlo (in dimensions $d=2,3$), and Bethe Ansatz (in $d=1$). We establish a low-temperature enhancement of the double occupancy $D$ at stromg coupling as a local probe of strong AF correlations accessible in cold-atom experiments [1]. As a function of entropy $s=S/(N k_{\text{B}})$, $D$ is nearly universal with respect to dimensionality, with a minimum in $D(s)$ at $s\approx \log(2)$ [2]. The quantum AF Heisenberg regime at $s\lesssim \log(2)$, driven by an abrupt gain in kinetic energy and with clear signatures also in the next-nearest neighbor correlation function, should be in immediate experimental reach. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve $s<\log(2)/2$ (on a cubic lattice) and should consider lower dimensions, for which the AF effects are larger, or even use dimensionality (as well as frustration) as a tunable parameter.

[1] E. V. Gorelik, I. Titvinidze, W. Hofstetter, M. Snoek, and N. Bl\"umer, Phys. Rev. Lett. {\bf 105}, 065301 (2010).

[2] E. V. Gorelik, T. Paiva, R. Scalettar, A. Kl\"umper, and N. Bl\"umer, arXiv:1105.3356v1.
	
