Universality of Charge and Spin Response in Doped Antiferromagnets

Recent results for the finite-temperature static and dynamical properties of the planar $t-J$ model, obtained by a novel numerical method for small correlated systems, are reviewed. Of particular interest are $T>0$ charge and spin response functions: optical conductivity $\sigma(\omega)$ and spin susceptibility $\chi(\vec q,\omega)$, which show very universal features at intermediate doping. In spin dynamics the universality is best seen in the local spin correlation function, which appears to be $T$-independent and only weakly doping dependent. Results apply directly to the inelastic neutron scattering and to the NMR relaxation experiments in cuprates. Analysing $\sigma(\omega)$ we find that the current correlation function $C(\omega)$ is nearly $T$- and moreover $\omega$-independent in the regime $T <J$, leading to the $\sigma(\omega)$ behavior, very close to the marginal Fermi liquid concept and experiments. These properties are interpreted in connection with the large entropy, related to the large degeneracy of the low-lying states and quantum frustration in the doped antiferromagnets. On the other hand, results for the uniform susceptibility $\chi_0(T)$, as well as for the $\sigma(\omega)$, reveal qualitative changes on entering the underdoped regime.