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.
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.
The interplay between spin and charge degrees of freedom arising from doping a Mott insulating quantum spin liquid (QSL) has been a topic of research for several decades. Calculating properties of these fractionalized metallic states in single-band models are generally restricted to mean-field patron descriptions and small fluctuations around these states, which are insufficient for quantitative comparison of observables to measurements performed in strongly-correlated systems. In this work, we numerically study a class of correlated electronic wavefunctions which support fractionalized spin and charge excitations and which fully take into account gauge fluctuations through the enforcement of local Hilbert space constraints. By optimizing the energy of these wavefunctions against the hole-doped Fermi Hubbard Hamiltonian, we obtain a variational ansatz for describing the low-energy physics of this model. We compare measurements of hole-induced spin-spin correlation functions to measurements taken in low temperature cold-atom simulations of the Hubbard model and find quantitative agreement between the two. In particular, we demonstrate the emergence of magnetic polaron correlations in these metallic states.
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 employ a family of ancilla qubit variational wave functions [Y.-H. Zhang and S. Sachdev, Phys. Rev. Res. 2 , 023172 (2020)] to describe the polaronic correlations in the pseudogap metal phase of a hole-doped 2D Fermi–Hubbard model. Comparison to ultracold atom quantum simulator data [J. Koepsell et al ., Science 374 , 82 (2021)] reveals both qualitative and quantitative agreement with the numerical analysis from half-filling up to 80% hole-doping, capturing the crossover from the polaronic regime to the Fermi liquid observed around 40% doping.
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.
Solid state physics, a very broad field in natural science, aims to explain physical properties of materials modeled as a many-body ensemble of the order of ∼ 10^23 interacting particles. For interacting metallic systems, one of the most powerful tools for unraveling the consequences of the collective interaction is the Fermi liquid theory. While still being an approximation, it excellently models many materials especially in the low-temperature and low-energy regime by treating themany-body problem as being equivalent to effectively non-interacting ”particles”, which is done by introducing the concept of quasiparticles. During the last few decades, several exotic phases of matter have been discovered, which originate from strong Coulomb interactions between the electrons, whose description is beyond the Fermi liquid theory. This thesis addresses the question of the validity of Fermi liquid theory once a single hole is introduced into an antiferromagnet with completely localized spins due to the strong interactions. Here, the most-studied case concerns the so-called 2D t − J model, which hosts a well-defined quasiparticle, the spin polaron. Focusing on a more tractable case, the t − Jz model without quantum spin fluctuations, we study the stability of the spin polaron solution once the nextnearest neighbor hopping t′ is introduced into the system. We focus on observations at the Γ-point and the X-point of systems with fixed Jz = 0.4t and varying t′ ∈ [−0.5t, 0.5t]. The model is numerically solved using exact diagonalization on finite-size lattices of up to 32 sites. A study of the quasiparticle weight under finite-size scaling reveals an “anomalous” regime at the Γ-point fort′ ≤ −0.3t, indicated by a vanishing quasiparticle weight. In order to characterize the low-energy dynamics within this “anomalous” regime, we investigated the spin correlation centered around the hole, as well as the magnon number distribution of a single-doped 20-site system. Based on the results, we present a preliminary picture of the antiferromagnetic ground state doped with one hole within that “anomalous” regime (t′ ≤ −0.3t) that deviates from the standard spin polaron as the cloud of magnetic fluctuations, typically localized around the hole, delocalizes over the whole finite-size lattice. Consequently, such systems show a weakly suppressed antiferromagnetic configuration under single-hole doping.
Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems.In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity.In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons.Measuring the density-and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation.At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling.Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.