Density response of the t-J model and renormalization of breathing and half-breathing phonon modes: A slave-fermion calculation

The density fluctuation spectrum $N({\bf k},\omega)$ is calculated for the t-J model in the low-doping regime using a slave-fermion method for the constrained fermions. The obtained results for $N({\bf k},\omega)$ are in good agreement with diagonalization results. The density response is characterized by incoherent, momentum dependent spectral functions reaching up to energies $\sim 8t$ and a low-energy structure at energy $\sim J$ due to transitions in the quasiparticle band. $N({\bf k},\omega)$ is shown to lead to a strong renormalization of planar bond-streching and breathing phonon modes with a large phonon linewidth at intermediate momenta caused by the low-energy response. Our results are consistent with recent neutron scattering data, showing the peculiar behavior of these modes.