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

We verify signatures of antiferromagnetic (AF) correlations in the double occupancy D [Gorelik et al., PRL 105, 065301 (2010)] and study their dimensional dependence using direct quantum Monte Carlo in dimensions d=2,3 and Bethe Ansatz in d=1. We find quantitative agreement with dynamical mean-field theory (DMFT) in the cubic case and qualitative agreement down to d=1. As a function of entropy s=S/(N k_B), D is nearly universal with respect to d; the minimum in D(s) approaches s=log(2) at strong coupling, as predicted by DMFT. 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.