The competition between antiferromagnetism and hole motion in two-dimensional Mott insulators lies at the heart of a doping-dependent transition from an anomalous metal to a conventional Fermi liquid. We observe such a crossover in Fermi-Hubbard systems on a cold-atom quantum simulator and reveal the transformation of multipoint correlations between spins and holes upon increasing doping at temperatures around the superexchange energy. Conventional observables, such as spin susceptibility, are furthermore computed from the microscopic snapshots of the system. Starting from a magnetic polaron regime, we find the system evolves into a Fermi liquid featuring incommensurate magnetic fluctuations and fundamentally altered correlations. The crossover is completed for hole dopings around 30%. Our work benchmarks theoretical approaches and discusses possible connections to lower-temperature phenomena.
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
ncr(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.
We study the evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fermi arcs, in-gap states, Lifshitz transitions, and non-Fermi liquids appears as natural consequences of this global interference in the frequency space.