Metal to insulator crossover in the repulsive Fermi-Hubbard model probed by static correlations

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 $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\kappa}}=\frac{\ensuremath{\partial}n}{\ensuremath{\partial}\ensuremath{\mu}}$ in comparison with the low-energy single-particle density of states $N(\ensuremath{\omega})$. (2) At finite doping, although $N(\ensuremath{\omega})$ remains gapless, a sign change in $\frac{\ensuremath{\partial}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\kappa}}}{\ensuremath{\partial}T}$ 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.