Charge dynamics and optical conductivity of the t-J model
  The dynamic charge susceptibility and the optical conductivity are calculated in the planar t-J model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped sound-like mode for small wave vectors and a broad high energy peak ($\sim t$) for large momenta. The study of the optical conductivity 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 charge carriers, extra absorbtions arise starting at a frequency $\omega \agt J$. The obtained results are in a good agreement with exact diagonalization studies. 
G. Jackeli and N. M. Plakida