Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization

All eigenstates and eigenvalues are determined for the spin- XXZ chain H=2J${\sum }_{\mathrm{i}}$(${\mathrm{S}}_{\mathrm{i}}^{\mathrm{x}}$ ${\mathrm{S}}_{\mathrm{i}+1\mathrm{}}^{\mathrm{x}}$+${\mathrm{S}}_{\mathrm{i}}^{\mathrm{y}}$ ${\mathrm{S}}_{\mathrm{i}+1\mathrm{}}^{\mathrm{y}}$+Δ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{z}}$ ${\mathrm{S}}_{\mathrm{i}+1\mathrm{}}^{\mathrm{z}}$) for rings with up to N=16 spins, for anisotropies Δ=0, cos (0.3π), and 1. The dynamic spin pair correlations 〈${\mathrm{S}}_{\mathrm{l}+\mathrm{n}}^{\mathrm{\mu }}$(t)${\mathrm{S}}_{\mathrm{l}}^{\mathrm{\mu }}$〉, (μ=x,z), the dynamic structure factors ${\mathrm{S}}^{\mathrm{\mu }}$(q,ω), and the intermediate structure factors ${\mathrm{I}}^{\mathrm{\mu }}$(q,t) are calculated for arbitrary temperature T. It is found that for all T, ${\mathrm{S}}^{\mathrm{z}}$(q,ω) is mainly concentrated on the region |ω|${\mathrm{\varepsilon }}_2$(q), where ${\mathrm{\varepsilon }}_2$(q) is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors ${\mathrm{I}}^{\mathrm{\mu }}$(q,t) for Δ≠0 show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin-correlation functions do not display the long-time signatures of spin diffusion.