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 [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. Secondly, 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
[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 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-like 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.Comment: 19 pages, 8 figure
