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We study the magnetic and charge dynamical response of a Hubbard model in atwo-leg ladder geometry using the density matrix renormalization group (DMRG)method and the random phase approximation within the fluctuation-exchangeapproximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture themain features of the magnetic response from weak up to intermediate Hubbardrepulsion for doped ladders, when compared with the numerically exact DMRGresults. However, while at weak Hubbard repulsion both the spin and chargespectra can be understood in terms of weakly-interacting electron-holeexcitations across the Fermi surface, at intermediate coupling DMRG showsgapped spin excitations at large momentum transfer that remain gapless withinthe RPA+FLEX approximation. For the charge response, RPA+FLEX can onlyreproduce the main features of the DMRG spectra at weak coupling and highdoping levels, while it shows an incoherent character away from this limit.Overall, our analysis shows that RPA+FLEX works surprisingly well for spinexcitations at weak and intermediate Hubbard $U$ values even in the difficultlow-dimensional geometry such as a two-leg ladder. Finally, we discuss theimplications of our results for neutron scattering and resonant inelastic x-rayscattering experiments on two-leg ladder cuprate compounds.

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: comparing DMRG and RPA+FLEX results