High-energy magnon dispersion in the half-filled Hubbard model: A comparison with La${}_2$CuO${}_4$

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 $U\mathrm{/}t<8$, 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 $U\mathrm{/}t$ and charge fluctuations in the cuprate materials.