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(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(k, omega) are in good agreement with d iagonalization results. The density response is characterized by incoherent , momentum dependent spectral functions reaching up to energies similar to 8t and a low-energy structure at energy similar to J due to transitions in the quasiparticle band. N(k, omega) is shown to lead to a strong renormaliz ation of planar bond-streching and breathing phonon modes with a large phon on linewidth at intermediate momenta caused by the low-energy response. Our results are consistent with recent neutron scattering data, showing the pe culiar behavior of these modes.