Dynamical correlations of spin-1/2 chains

We show that the long-time behavior of the self-correlation function $\langle0|S_j^z(t)S_j^z(0)|0\rangle$ of the S=1/2 XXZ model in the critical regime is dominated by high-energy excitations. We relate the exponents of the long-time decay to phase shifts which are known exactly from the Bethe ansatz. The same exponents are connected with the singularities of the dynamical structure factor $S^{zz}(q,\omega)$. By combining the analytical results with the time-dependent density matrix renormalization group (tDMRG), we calculate $S^{zz}(q,\omega)$ to very high precision.