Dynamic Correlation Functions for Quantum Spin Chains

New exact results are presented on the long-time asymptotic expansions of the $T=0$ autocorrelation functions, and on the leading singularities of their frequency-dependent Fourier transforms, for the one-dimensional S=1/2 isotropic XY model and the S=1/2 transverse Ising model at the critical field. High-precision numerical calculations of the latter functions are also given, and experiments are proposed to observe the functional behaviors that are found.