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=12 isotropic XY model and the S=12 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.