The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.
The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction (
T-
U) plane. With increasing
U, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing
U. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.
The Hubbard model at temperatures above the Néel transition, despite being a paramagnet, can exhibit rich physics due to the interplay of Fermi surface, on-site interaction U and thermal fluctuations. Nevertheless, the understanding of the crossover physics remains only at a qualitative level, because of the intrinsically smooth behavior. Employing an improved variant of the numerically exact auxiliary-field quantum Monte Carlo algorithm equipped with numerical analytic continuation, we obtain a broad variety of thermodynamic and dynamical properties of the three-dimensional Hubbard model at half filling, quantitatively determine the crossover boundaries, and observe that the metal-insulator crossover regime, in which antiferromagnetic spin correlations appear strongest, exists over an extended regime in between the Fermi liquid for small U and the Mott insulator for large U. In particular, the location of the most rapid suppression of double occupancy as U increases, is found to fully reside in the metallic Fermi liquid regime, in contrast to the conventional intuition that it is a representative feature for entering the Mott insulator. Beside providing a reliable methodology for numerical study of crossover physics, our work can also serve as a timely and important guideline for the most recent optical lattice experiments.
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 thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.
Cold atom systems provide a rich platform to realize strongly interacting condensed matter systems, and recent progress in fluorescence imaging technique has enabled identification of nontrivial doublon, singlon, and holon correlation functions. We show that these correlators can be used to identify the conditions under which local moments form in an interacting electronic system. Toward this end, we report a Determinantal Quantum Monte Carlo (DQMC) study of such correlation functions in the two-dimensional repulsive Fermi Hubbard model on a square lattice as a function of doping, interaction strength and temperature. We find definite signatures of the crossover from small U(band regime) to large U(correlated insulator regime). Our key findings are: (1) An opening of a charge gap in the thermodynamic density of states is accompanied by the appearance of temperature insensitive points in the equation of state at finite doping, which can be used to distinguish the band regime in cold atom experiments. (2) Nearest neighbor doublon holon correlations track the opening of charge gap; these compete with density correlations to generate moment moment correlations that show different behavior in the metallic and correlated insulator regime. (3) Non local correlation functions can be used to distinguish between the two regimes, both at and away from half filling. Our results allow comparisons of different correlation functions with recent experimental findings and guide further experimental investigations.