All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{ i}^{ x} S_{ i + 1}^{ x} + S_{ i}^{ y} S_{ i + 1}^{ y} + \Delta S_i^z S_{ i + 1}^{ z})$ for rings with up to N=16 spins, for anisotropies $\Delta=0 , \cos(0.3\pi)$, and 1. The dynamic spin pair correlations $< S_{ l+n}^{ \mu}(t) S_l^{ \mu} > , (\mu=x,z)$, the dynamic structure factors $S^{ \mu}(q,\omega)$, and the intermediate structure factors $I^{ \mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{ z}(q,\omega)$ is mainly concentrated on the region $|\omega| < \varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{ \mu}(q,t)$ for $\Delta \neq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.
Categories: cond-mat.stat-mech