Exact formulas for the singularities of the dynamical structure factor, $S^{zz}(q,\omega )$, of the $S=1/2$ $xxz$ spin chain at all $q$ and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the phase shifts which are known exactly from the Bethe ansatz solution. We also study the long-time asymptotics of the self-correlation function $⟨0|S_j^z(t)S_j^z(0)|0⟩$. Utilizing these results to supplement very accurate time-dependent density matrix renormalization group, for short to moderate times, we calculate $S^{zz}(q,\omega )$ to very high precision.

• Received 6 September 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.027206