We use quantum Monte Carlo methods and single-mode approximation to study the magnon dispersion in the 2D half-filled Hubbard and phonon-coupled Heisenberg models. We find that in the Hubbard model with $U/t< 8$, high-energy magnon dispersion is similar to those observed in inelastic neutron scattering experiments in ${La}_2{CuO}_4$. On the other hand, our studies of a 2D Heisenberg model coupled to dynamic optical bond phonons, fails to reproduce the experimental dispersion. These results can be interpreted as evidence for intermediate $U/t$ and charge fluctuations in the cuprate materials.
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