Charge dynamics of t-J model and anomalous bond-stretching phonons in cuprates

The density response of a doped Mott-Hubbard insulator is discussed starting from the t-J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q,ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin-charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q,ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δ t related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π ,0) direction, describes the strong renormalization and anomalous damping of the highest bond-stretching phonons in La2−xSrxCuO4. Dedicated to Ferdinando Mancini on the occasion of his 60th birthday published in AIP Conference Proceedings 695: “Highlights in Condensed Matter Physics”, ed. A. Avella et al. (AIP, New York, 2003)