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, ω) 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, ω) are in good agreement with diagonalization results. The density response is characterized by incoherent, momentum dependent spectral functions reaching up to energies ∼ 8t and a low-energy structure at energy ∼ J due to transitions in the quasiparticle band. N(k, ω) 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.