Charge dynamics and optical conductivity of the t-J model

The dynamic charge susceptibility and the optical conductivity are calculat ed in the planar t-J model within the memory function method, working direc tly in terms of Hubbard operators. The density fluctuation spectrum consist s of a damped soundlike mode for small wave vectors and a broad high energy peak(similar to t) for large momenta. The study of the optical conductivit y shows that electron scattering from spin fluctuations leads to the Drude- frequency dependent relaxation rate which exhibits a crossover from omega(3 /2) behavior at low frequencies (omega<2/mu/), to a linear omega dependence for frequencies larger than 2/mu/. Due to the spin-polaron nature of charg e carriers, extra absorptions arise starting at a frequency omega greater t han or similar to J. The obtained results are in a good agreement with exac t diagonalization studies. [S0163-1829(99)08431-3].