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We study the relation between the microscopic properties of a many-bodysystem and the electron spectra, experimentally accessible by photoemission. Ina recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the"fluctuation diagnostics" approach, to extract the dominant wave vectordependent bosonic fluctuations from the electronic self-energy. Here, we firstreformulate the theory in terms of fermionic modes, to render its connectionwith resonance valence bond (RVB) fluctuations more transparent. Secondly, byusing a large-U expansion, where U is the Coulomb interaction, we relate thefluctuations to real space correlations. Therefore, it becomes possible tostudy how electron spectra are related to charge, spin, superconductivity andRVB-like real space correlations, broadening the analysis of an earlier work[Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogapphysics of the two-dimensional Hubbard model, studied in the dynamical clusterapproximation. We perform calculations for embedded clusters with up to 32sites, having three inequivalent K-points at the Fermi surface. We find that asU is increased, correlation functions gradually attain values consistent withan RVB state. This first happens for correlation functions involving theantinodal point and gradually spreads to the nodal point along the Fermisurface. Simultaneously a pseudogap opens up along the Fermi surface. We relatethis to a crossover from a Kondo-like state to an RVB-like localized clusterstate and to the presence of RVB and spin fluctuations. These changes arecaused by a strong momentum dependence in the cluster bath-couplings along theFermi surface. We also show, from a more algorithmic perspective, how thetime-consuming calculations in fluctuation diagnostics can be drasticallysimplified.

Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations