We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [O. Gunnarsson et al., Phys. Rev. Lett. 114, 236402 (2015)], we introduced the “fluctuation diagnostics” approach to extract the dominant wave-vector-dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes to render its connection with resonance valence bond (RVB) fluctuations more transparent. Second, by using a large-$U$ expansion, where $U$ is the Coulomb interaction, we relate the fluctuations to real-space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity, and RVB-like real-space correlations, broadening the analysis of an earlier work [J. Merino and O. Gunnarsson, Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent $\mathbf{K}$ points at the Fermi surface. We find that as $U$ is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously, a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-type state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.

中文翻译：

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电子光谱的补充视图：从波动诊断到真实空间相关

我们研究了多体系统的微观性质与电子光谱之间的关系，该电子光谱可以通过光发射实验获得。在最近的一篇论文中[O. Gunnarsson等。，物理 莱特牧师 114，236402（2015）]中，我们引入了“波动诊断”的方法来提取从电子自能主波矢量依赖性玻色子的波动。在这里，我们首先根据铁离子模式重新构建该理论，以使其与共振价键（RVB）波动的联系更加透明。其次，通过使用$ü$ 扩展，在哪里 $ü$是库仑相互作用，我们将波动与真实空间相关性关联起来。因此，研究电子光谱与电荷，自旋，超导性和类似RVB的真实空间相关性成为可能，从而拓宽了早期工作的分析范围[J. Merino和O. Gunnarsson，物理学。版本B 89，245130（2014）]。这种形式主义被应用到二维哈伯德模型的伪间隙物理学中，在动态簇近似中研究。我们对多达32个站点（其中三个不等价）的嵌入式集群执行计算$\mathbf{ķ}$指向费米表面。我们发现$ü$如果增加，则相关函数逐渐达到与RVB状态一致的值。这首先发生在涉及反结点的相关函数上，并沿费米表面逐渐扩展到结点。同时，伪间隙沿费米表面打开。我们将其与从近藤型态到RVB状的局部簇态的交叉以及RVB和自旋涨落的存在联系起来。这些变化是由于沿费米表面的簇状浴耦合中强烈的动量依赖性引起的。我们还将从更算法的角度展示如何显着简化波动诊断中的耗时计算。