  Estimating many-body effects that deviate from an independent particle
approach, has long been a key research interest in condensed matter physics.
Layered cuprates are prototypical systems, where electron-electron interactions
are found to strongly affect the dynamics of single-particle excitations. It is
however, still unclear how the electron correlations influence charge
excitations, such as plasmons, which have been variously treated with either
weak or strong correlation models. In this work, we demonstrate the hybridised
nature of collective valence charge fluctuations leading to dispersing
acoustic-like plasmons in hole-doped La$_{1.84}$Sr$_{0.16}$CuO$_{4}$ and
electron-doped La$_{1.84}$Ce$_{0.16}$CuO$_{4}$ using the two-particle probe,
resonant inelastic x-ray scattering. We then describe the plasmon dispersions
in both systems, within both the weak mean-field Random Phase Approximation
(RPA) and strong coupling $t$-$J$-$V$ models. The $t$-$J$-$V$ model, which
includes the correlation effects implicitly, accurately describes the plasmon
dispersions as resonant excitations outside the single-particle intra-band
continuum. In comparison, a quantitative description of the plasmon dispersion
in the RPA approach is obtained only upon explicit consideration of
re-normalized electronic band parameters. Our comparative analysis shows that
electron correlations significantly impact the low-energy plasmon excitations
across the cuprate doping phase diagram, even at long wavelengths. Thus,
complementary information on the evolution of electron correlations, influenced
by the rich electronic phases in condensed matter systems, can be extracted
through the study of two-particle charge response.
