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

摘要

The density response of a doped Mott-Hubbard insulator is discussed startingfrom the t-J model in a slave boson 1/N representation. In leading order O(1)the density fluctuation spectra $N({\bf q},\omega)$ are determined by anundamped collective mode at large momentum transfer, in striking disagreementwith results obtained by exact diagonalization, which reveal a very broaddispersive peak, reminescent of strong spin-charge coupling. The 1/Ncorrections introduce the polaron character of the bosonic holes moving in auniform RVB background. The resulting $N({\bf q},\omega)$ captures all featuresobserved in diagonalization studies, fulfills the appropriate sum rules, andapart from the broadening of the collective mode shows a new low energy featureat the energy $\chi J+\delta t$ related to the polaron motion in the spinonbackground. It is further shown that the low energy structure, which isparticularly pronounced in $(\pi,0)$ direction, describes the strongrenormalization and anomalous damping of the highest bond-stretching phonons inLa$_{2-x}$Sr$_x$CuO$_4$.