Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet

The exact expression derived by Bougourzi, Couture, and Kacir for the 2-spinon contribution to the dynamic spin structure factor $S_{zz}(q,\omega)$ of the one-dimensional $S$=1/2 Heisenberg antiferromagnet at $T=0$ is evaluated for direct comparison with finite-chain transition rates ($N \leq 28$) and an approximate analytical result previously inferred from finite-$N$ data, sum rules, and Bethe-ansatz calculations. The 2-spinon excitations account for 82.18\% of the total intensity in $S_{zz}(q,\omega)$. The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the 2-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and $q$-dependent susceptibility are determined via sum rules.