Universal Charge and Spin Response in Optimally Doped Antiferromagnets

Charge and spin response in the planar $t-J$ model at finite temperatures are investigated numerically, in the regime corresponding to cuprates at intermediate doping. We show that the local spin correlation function is $T$-independent, leading to $\chi''(\omega<J) \propto \tanh (\omega/2 T)$. The current correlation function $C(\omega)$ appears to be $T$- as well as $\omega$-independent, and the optical conductivity $\sigma \propto (1- e^{-\omega/T})/\omega$. Such anomalous response functions are brought in connection with the large entropy persisting at $T<J$.