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 ${\chi }^{\prime \prime }(\omega <J)\propto \tanh \left(\omega /2T\right)$. The current correlation function $C\left(\omega \right)$ appears to be $T$ as well as $\omega$ independent, and the optical conductivity $\sigma \propto \left({1-e}^{-\omega /T}\right)/\omega$. Such anomalous response functions are brought in connection with the large entropy persisting at $T<J$.