Charge Dynamics in the Planar t-J Model

The finite-temperature optical conductivity $\sigma(\omega)$ in the planar $t-J$ model is analysed using recently introduced numerical method based on the Lanczos diagonalization of small systems (up to 20 sites), as well as by analytical approaches, including the method of frequency moments and the retraceable-path approximation. Results for a dynamical mobility of a single hole at elevated temperatures $T>t$ reveal a Gaussian-like $\mu(\omega)$ spectra, however with a nonanalytical behavior at low $\omega$. In the single hole response a difference between the ferromagnetic (J=0) and the antiferromagnetic ($J>0$) polaron shows up at $T<J$. At larger dopings numerical results in studied systems are consistent with the thermodynamical behavior for $T>T^*\ge 0.1~t$. $\sigma(\omega)$ spectra show a non-Drude falloff at large frequencies. In particular for `optimum' doping $n_h \sim 0.2$ we obtain in the low-$\omega,T$ regime the relaxation rate $\tau^{-1} \sim 0.6 (\omega+\xi T)$ with $\xi \sim 3$, being consistent with the marginal Fermi liquid concept and experiments. Within the same regime we reproduce the nearly linear variation of dc resistivity $\rho$ with $T$. This behavior is weakly dependent on $J$, provided that $J<t$.