Ordering and fluctuations in the ground state of the one-dimensional and two-dimensionalS=1/2XXZantiferromagnets: A study of dynamical properties based on the recursion method

The recursion method is applied to the T=0 dynamics of the S=1/2 XXZ model on a linear chain and a square lattice. By means of new calculational techniques for the analysis of the continued-fraction coefficients pertaining to specific dynamical quantities, we obtain reliable information on the type of ordering in the ground state, on the size of gaps in the dynamically relevant excitation spectrum, on the bandwidths of dominant structures in spectral densities, on the exponents of infrared singularities, and on the detailed shape of spectral-weight distributions. We investigate some characteristic properties of the dynamic structure factors ${\mathit{S}}_{\mathrm{\mu }\mathrm{\mu }}$(q,ω) and the spin autocorrelation functions ${\mathit{S}}^{\mathrm{\mu }\mathrm{\mu }}$(ω)=${\mathit{N}}^{\mathrm{-}1}$ t${sum}_{\mathbf{q}}$ ${\mathit{S}}_{\mathrm{\mu }\mathrm{\mu }}$(q,ω), specifically their dependence on the uniaxial anisotropy, i.e., on the parameter which controls the type of ordering and the amount of quantum fluctuations in the ground state. We find, for example, that the different degrees of ordering in the planar regime of the one-dimensional and two-dimensional systems (criticality versus antiferromagnetic long-range order) have characteristic signatures in the dynamical properties which are conspicuously displayed in our results.