The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state-of-the-art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate-temperature metallic regime, and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo methods) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes. Based on this analysis, we explain how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime. We also critically discuss whether imaginary-time methods are able to capture the non-Fermi-liquid singularities of this fully nested system.

中文翻译：

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跟踪自旋波动的足迹：二维哈伯德模型的多方法，多信使研究

哈伯德模型代表了相互作用的量子系统和电子相关性的基本模型。使用弱耦合的二维半填充哈伯德模型作为测试基础，我们对一整套最先进的量子多体方法进行了比较研究。冷却到其绝缘反铁磁基态后，该模型具有一系列丰富的不同物理状态，并在高温非相干状态，中温金属状态和低温绝缘状态之间具有交叉关系，其中伪绝缘由反铁磁波动产生。我们通过计算探测准粒子性质和磁相关性的几个可观察物，评估每种方法正确解决这些物理状态和交叉的能力，有两种数值精确的方法（图解法和行列式量子蒙特卡洛方法）作为基准。通过将计算结果和分析见解相结合，我们阐明了自旋波动在每种情况下的性质和作用。基于此分析，我们解释了准粒子如何与越来越远的反铁磁相关性共存，以及为什么发现了动态平均场理论可以提供金属态中局部量的非常精确的近似值。我们还批判性地讨论了虚时方法是否能够捕获此完全嵌套系统的非费米液体奇点。我们阐明了自旋波动在每种情况下的性质和作用。基于此分析，我们解释了准粒子如何与越来越远的反铁磁相关性共存，以及为什么发现了动态平均场理论可以提供金属态中局部量的非常精确的近似值。我们还批判性地讨论了虚时方法是否能够捕获此完全嵌套系统的非费米液体奇点。我们阐明了自旋波动在每种情况下的性质和作用。基于此分析，我们解释了准粒子如何与越来越远的反铁磁相关性共存，以及为什么发现了动态平均场理论可以提供金属态中局部量的非常精确的近似值。我们还批判性地讨论了虚时方法是否能够捕获此完全嵌套系统的非费米液体奇点。