Time-dependent spin autocorrelation functions and their spectral densities for the semi-infinite one-dimensional 1 XY and XXZ models at T= oo are determined in part by rigorous calculations in the fermion representation and in part by the recursion method in the spin representation. Boundary effects yield valuable new insight into the different dynamical processes which govern the transport of spin fluctuations in the two models. The results obtained for the X X X model bear the unmistakable signature of spin diffusion in the form of a squareroot infrared divergence in the spectral density.
We present a study on the nature of the dynamical on-site spin-pair correlation in an s=1/2 isotropic Heisenberg chain at T=\ensuremath{\infty} using the Mori-Lee formalism for solving the Heisenberg equation of motion and the direct summation method of evaluating infinite continued fractions. Our results are consistent with existing short-time analyses and support a power-law decay of the spin-pair correlations. Our study reveals that the frequency spectra corresponding to the on-site dynamical correlations can be seen as consisting of a Gaussian central peak presumably arising from the XY part of the Hamiltonian and a second broad finite frequency peak, which probably arises from the Ising part of the Hamiltonian and is slightly shifted toward a higher frequency than the Ising frequency.