LAUSR

We provide a unified interpretation of both paramagnon and plasmon modes in high-Tc copperoxides, and verify it quantitatively against available resonant inelastic x-ray scattering (RIXS) data across the hole-doped phase diagram. Three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using VWF+1/Nf approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors (1/Nf ). We show that intense paramagnons persist along the anti-nodal line from the underdoped to overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to anti-phase oscillations on neighboring CuO2 planes. The theoretical spinand charge excitation energies reproduce semi-quantitatively RIXS data for (Bi,Pb)2(Sr,La)2CuO6+δ. The present VWF+1/Nf analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-Tc cuprates as strongly correlated systems.