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 $\tilde{\kappa }=\frac{\partial n}{\partial \mu }$ in comparison with the low-energy single-particle density of states $N\left(\omega \right)$. (2) At finite doping, although $N\left(\omega \right)$ remains gapless, a sign change in $\frac{\partial \tilde{\kappa }}{\partial T}$ marks a transition from insulating to metallic behavior at a critical density $n_{\text{cr}}(U,T)$. (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.

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• Cold gases in optical lattices
• Metal-insulator transition
• Quantum correlations, foundations & formalism
• Strongly correlated systems
• Hubbard model
• Non-Fermi-liquid theory
• Quantum Monte Carlo