Two-spinon dynamic structure factor of the one-dimensional s= Heisenberg antiferromagnet

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Abstract
The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q,ω) of the one-dimensional s=1/2 Heisenberg antiferromagnet at T=0 is evaluated for direct comparison with finite-chain transition rates (N⩽28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q,ω). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-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. The impact of the non-two-spinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q,ω) is studied on the basis of finite-size data.