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Physical review. B./Physical review. B

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

Sayantan Roy, Sameed Pervaiz, Thereza Paiva, Nandini Trivedi

Published Sep 29, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1103/yc85-b7tz

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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.
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 (TTT-UUU) plane. With increasing UUU, 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 UUU. 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.
We investigate finite-temperature precursors of Mottness in the repulsive Hubbard model above the spin-ordering temperature, using numerically exact determinant quantum Monte Carlo. We show that the finite-temperature crossover is accompanied by a pronounced suppression of charge fluctuations, despite the presence of a gapless single-particle spectra, demonstrating that Mottness first emerges via two-particle response in an anomalous metallic regime, before appearing in single-particle spectral functions. We further show that a gap formation in the density of states occurs through momentum-resolved redistribution of spectral weight across the Brillouin zone, that begins at the onset of anomalous metallic regime, rather than through gap formation in single-particle spectral functions at individual momenta. Upon doping, the anomalous-metallic regime generates transport and spectroscopic signatures characteristic of doped Mott insulators. This shows that the transport and spectroscopic anomalies of the doped Hubbard model do not require the presence of a fully formed Mott insulator at half-filling, but instead originate from the strong charge-response renormalization and spectral-weight redistribution that develop within the precursor anomalous metallic regime at half-filling.
The 2D Hubbard model with nearest-neighbor hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using the diagrammatic Monte Carlo approach in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and nonlocal fluctuations in both channels are essential.
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.
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.