  To shed light on how electronic correlations vary across the phase diagram of
the cuprate superconductors, we examine the doping evolution of spin and charge
excitations in the single-band Hubbard model using determinant quantum Monte
Carlo (DQMC). In the single-particle response, we observe that the effects of
correlations weaken rapidly with doping, such that one may expect the random
phase approximation (RPA) to provide an adequate description of the
two-particle response. In contrast, when compared to RPA, we find that
significant residual correlations in the two-particle excitations persist up to
$40\%$ hole and $15\%$ electron doping (the range of dopings achieved in the
cuprates). These fundamental differences between the doping evolution of
single- and multi-particle renormalizations show that conclusions drawn from
single-particle processes cannot necessarily be applied to multi-particle
excitations. Eventually, the system smoothly transitions via a
momentum-dependent crossover into a weakly correlated metallic state where the
spin and charge excitation spectra exhibit similar behavior and where RPA
provides an adequate description.
