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Recent advances in fluorescence imaging have enabled direct measurements of doublon, singlon, and holon correlation functions in cold-atom experiments. We demonstrate that these correlators provide a powerful probe of the extended crossover from metallic to insulating behavior at intermediate and high temperatures. To this end, we carry out determinantal quantum Monte Carlo simulations of the two-dimensional repulsive Fermi-Hubbard model on a square lattice, varying doping, interaction strength U, and temperature T. Our results reveal clear signatures of a crossover from the metallic regime at small U to the Mott insulating regime at large U. Specifically, we note the following: (1) At half-filling, we distinguish three regimes (metallic, non-Fermi-liquid, and Mott insulating) by analyzing the temperature dependence of the thermodynamic density of states \~{}= in comparison with the low-energy single-particle density of states N (). (2) At finite doping, although N () remains gapless, a sign change in { \~{}} marks a transition from insulating to metallic behavior at a critical density n₂ₑ (U, T). (3) These crossovers can also be tracked using experimentally accessible correlators, such as density-density, moment-moment, and doublon-holon correlations, providing valuable diagnostics in settings where direct spectral information is difficult to obtain.
Roy et al. (Mon,) studied this question.