Thermodynamics vs. local density fluctuations in the   metal/Mott-insulator crossover
  The crossover between a metal and a Mott insulator leads to a localization of fermions from delocalized Bloch states to localized states. We experimentally study this crossover using fermionic atoms in an optical lattice by measuring thermodynamic and local (on--site) density correlations. In the metallic phase at incommensurable filling we observe the violation of the local fluctuation--dissipation theorem indicating that the thermodynamics cannot be explained by local observables. In contrast, in the Mott-insulator we observe the convergence of local and thermodynamic fluctuations indicating the absence of long--range density-density correlations. 
J. H. Drewes, E. Cocchi, L. A. Miller, C. F. Chan, D. Pertot, F.   Brennecke, and M. K\"ohl
cond-mat.quant-gas